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Here minLines allows to set minimum height for the textView (to resist height minimizing by AutoLayout with UITableViewAutomaticDimension).

moveRowAtIndexPath:indexPath: with the same indexPath starts tableViewCell height re-calculation and re-layout.

performWithoutAnimation: removes side-effect (tableView content offset jumping on starting new line while typing).

It is important to preserve relativeFrameOriginY (not contentOffsetY!) during cell update because contentSize of the cells before the current cell could be change by autoLayout calculus in unexpected way. It removes visual jumps on system hyphenation while typing long words.

==================================================================================

• Here minLines allows to set minimum height for the textView (to resist height minimizing by AutoLayout with UITableViewAutomaticDimension).

• moveRowAtIndexPath:indexPath: with the same indexPath starts tableViewCell height re-calculation and re-layout.

• performWithoutAnimation: removes side-effect (tableView content offset jumping on starting new line while typing).

• It is important to preserve relativeFrameOriginY (not contentOffsetY!) during cell update because contentSize of the cells before the current cell could be change by autoLayout calculus in unexpected way. It removes visual jumps on system hyphenation while typing long words.

• Note that you shouldn't set the property estimatedRowHeight! The following doesn't work

   self.tableView.estimatedRowHeight = UITableViewAutomaticDimension;
  

  Use only tableViewDelegate method.

==========================================================================

@protocol TextInputTableViewCellDelegate <NSObject>
@optional
- (void)textInputTableViewCellTextWillChange:(TextInputTableViewCell *)cell;
- (void)textInputTableViewCellTextDidChange:(TextInputTableViewCell *)cell;
@end

@interface TextInputTableViewCell : UITableViewCell
@property (nonatomic, weak) id<TextInputTableViewCellDelegate> delegate;
@property (nonatomic, readonly) UITextView *textView;
@property (nonatomic) NSInteger minLines;
@property (nonatomic) lastRelativeFrameOriginY;
@end


#import "TextInputTableViewCell.h"

@interface TextInputTableViewCell () <UITextViewDelegate> {
    NSLayoutConstraint *_heightConstraint;
}
@property (nonatomic) UITextView *textView;
@end

@implementation TextInputTableViewCell

- (id)initWithStyle:(UITableViewCellStyle)style reuseIdentifier:(NSString *)reuseIdentifier {
    self = [super initWithStyle:style reuseIdentifier:reuseIdentifier];
    if (self) {
        self.selectionStyle = UITableViewCellSelectionStyleNone;
    
        _textView = [UITextView new];
        _textView.translatesAutoresizingMaskIntoConstraints = NO;
        _textView.delegate = self;
        _textView.scrollEnabled = NO;
        _textView.font = CELL_REG_FONT;
        _textView.textContainer.lineFragmentPadding = 0.0;
        _textView.textContainerInset = UIEdgeInsetsZero;
        [self.contentView addSubview:_textView];
    
        [self.contentView addConstraints: [NSLayoutConstraint constraintsWithVisualFormat:@"H:|-[view]-|" options:nil metrics:nil views:@{@"view": _textView}]];
        [self.contentView addConstraints: [NSLayoutConstraint constraintsWithVisualFormat:@"V:|-[view]-|" options:nil metrics:nil views:@{@"view": _textView}]];

        _heightConstraint = [NSLayoutConstraint constraintWithItem: _textView
                         attribute: NSLayoutAttributeHeight
                         relatedBy: NSLayoutRelationGreaterThanOrEqual
                         toItem: nil
                         attribute: NSLayoutAttributeNotAnAttribute
                         multiplier: 0.0
                         constant: (_textView.font.lineHeight + 15)];
        _heightConstraint.priority = UILayoutPriorityRequired - 1;
        [_textView addConstraint:_heightConstraint];
    }
    return self;
}

- (void)prepareForReuse {
    [super prepareForReuse];    
    self.minLines = 1;
}

- (void)setMinLines:(NSInteger)minLines {
    _heightConstraint.constant = minLines * _textView.font.lineHeight + 15;
}

- (BOOL)textView:(UITextView *)textView shouldChangeTextInRange:(NSRange)range replacementText:(NSString *)text {
    if ([self.delegate respondsToSelector:@selector(textInputTableViewCellTextWillChange:)]) {
        [self.delegate textInputTableViewCellTextWillChange:self];
    }
    return YES;
}

- (void)textViewDidChange:(UITextView *)textView {
    if ([self.delegate respondsToSelector:@selector(textInputTableViewCellTextDidChange:)]) {
        [self.delegate textInputTableViewCellTextDidChange:self];
    }
}

@protocol TextInputTableViewCellDelegate <NSObject>
@optional
- (void)textInputTableViewCellTextWillChange:(TextInputTableViewCell *)cell;
- (void)textInputTableViewCellTextDidChange:(TextInputTableViewCell *)cell;
@end

@interface TextInputTableViewCell : UITableViewCell
@property (nonatomic, weak) id<TextInputTableViewCellDelegate> delegate;
@property (nonatomic, readonly) UITextView *textView;
@property (nonatomic) NSInteger minLines;
@property (nonatomic) CGFloat lastRelativeFrameOriginY;
@end


#import "TextInputTableViewCell.h"

@interface TextInputTableViewCell () <UITextViewDelegate> {
    NSLayoutConstraint *_heightConstraint;
}
@property (nonatomic) UITextView *textView;
@end

@implementation TextInputTableViewCell

- (id)initWithStyle:(UITableViewCellStyle)style reuseIdentifier:(NSString *)reuseIdentifier {
    self = [super initWithStyle:style reuseIdentifier:reuseIdentifier];
    if (self) {
        self.selectionStyle = UITableViewCellSelectionStyleNone;
    
        _textView = [UITextView new];
        _textView.translatesAutoresizingMaskIntoConstraints = NO;
        _textView.delegate = self;
        _textView.scrollEnabled = NO;
        _textView.font = CELL_REG_FONT;
        _textView.textContainer.lineFragmentPadding = 0.0;
        _textView.textContainerInset = UIEdgeInsetsZero;
        [self.contentView addSubview:_textView];
    
        [self.contentView addConstraints: [NSLayoutConstraint constraintsWithVisualFormat:@"H:|-[view]-|" options:nil metrics:nil views:@{@"view": _textView}]];
        [self.contentView addConstraints: [NSLayoutConstraint constraintsWithVisualFormat:@"V:|-[view]-|" options:nil metrics:nil views:@{@"view": _textView}]];

        _heightConstraint = [NSLayoutConstraint constraintWithItem: _textView
                         attribute: NSLayoutAttributeHeight
                         relatedBy: NSLayoutRelationGreaterThanOrEqual
                         toItem: nil
                         attribute: NSLayoutAttributeNotAnAttribute
                         multiplier: 0.0
                         constant: (_textView.font.lineHeight + 15)];
        _heightConstraint.priority = UILayoutPriorityRequired - 1;
        [_textView addConstraint:_heightConstraint];
    }
    return self;
}

- (void)prepareForReuse {
    [super prepareForReuse];    
    self.minLines = 1;
}

- (void)setMinLines:(NSInteger)minLines {
    _heightConstraint.constant = minLines * _textView.font.lineHeight + 15;
}

- (BOOL)textView:(UITextView *)textView shouldChangeTextInRange:(NSRange)range replacementText:(NSString *)text {
    if ([self.delegate respondsToSelector:@selector(textInputTableViewCellTextWillChange:)]) {
        [self.delegate textInputTableViewCellTextWillChange:self];
    }
    return YES;
}

- (void)textViewDidChange:(UITextView *)textView {
    if ([self.delegate respondsToSelector:@selector(textInputTableViewCellTextDidChange:)]) {
        [self.delegate textInputTableViewCellTextDidChange:self];
    }
}

==================================================================================

If one doesn't mind against weak binding between tableView and tableViewCell and updating geometry of the tableView from tableViewCell, it is possible to upgrade TextInputTableViewCell class above:

@interface TextInputTableViewCell : UITableViewCell
@property (nonatomic, weak) id<TextInputTableViewCellDelegate> delegate;
@property (nonatomic, weak) UITableView *tableView;
@property (nonatomic, readonly) UITextView *textView;
@property (nonatomic) NSInteger minLines;
@end


#import "TextInputTableViewCell.h"

@interface TextInputTableViewCell () <UITextViewDelegate> {
    NSLayoutConstraint *_heightConstraint;
    CGFloat _lastRelativeFrameOriginY;
}
@property (nonatomic) UITextView *textView;
@end

@implementation TextInputTableViewCell

- (id)initWithStyle:(UITableViewCellStyle)style reuseIdentifier:(NSString *)reuseIdentifier {
    self = [super initWithStyle:style reuseIdentifier:reuseIdentifier];
    if (self) {
        self.selectionStyle = UITableViewCellSelectionStyleNone;
    
        _textView = [UITextView new];
        _textView.translatesAutoresizingMaskIntoConstraints = NO;
        _textView.delegate = self;
        _textView.scrollEnabled = NO;
        _textView.font = CELL_REG_FONT;
        _textView.textContainer.lineFragmentPadding = 0.0;
        _textView.textContainerInset = UIEdgeInsetsZero;
        [self.contentView addSubview:_textView];
    
        [self.contentView addConstraints: [NSLayoutConstraint constraintsWithVisualFormat:@"H:|-[view]-|" options:nil metrics:nil views:@{@"view": _textView}]];
        [self.contentView addConstraints: [NSLayoutConstraint constraintsWithVisualFormat:@"V:|-[view]-|" options:nil metrics:nil views:@{@"view": _textView}]];

        _heightConstraint = [NSLayoutConstraint constraintWithItem: _textView
                         attribute: NSLayoutAttributeHeight
                         relatedBy: NSLayoutRelationGreaterThanOrEqual
                         toItem: nil
                         attribute: NSLayoutAttributeNotAnAttribute
                         multiplier: 0.0
                         constant: (_textView.font.lineHeight + 15)];
        _heightConstraint.priority = UILayoutPriorityRequired - 1;
        [_textView addConstraint:_heightConstraint];
    }
    return self;
}

- (void)prepareForReuse {
    [super prepareForReuse];    
    self.minLines = 1;
    self.tableView = nil;
}

- (void)setMinLines:(NSInteger)minLines {
    _heightConstraint.constant = minLines * _textView.font.lineHeight + 15;
}

- (BOOL)textView:(UITextView *)textView shouldChangeTextInRange:(NSRange)range replacementText:(NSString *)text {
    
    _lastRelativeFrameOriginY = self.frame.origin.y - self.tableView.contentOffset.y;
    return YES;
}

- (void)textViewDidChange:(UITextView *)textView {

    NSIndexPath *indexPath = [self.tableView indexPathForCell:self];
    if (indexPath == nil) return;

    [UIView performWithoutAnimation:^{
        [self.tableView moveRowAtIndexPath:indexPath toIndexPath:indexPath];
    }];

    CGFloat contentOffsetY = self.frame.origin.y - _lastRelativeFrameOriginY;
    self.tableView.contentOffset = CGPointMake(self.tableView.contentOffset.x, contentOffsetY);

    CGRect caretRect = [self.textView caretRectForPosition:self.textView.selectedTextRange.start];
    caretRect = [self.tableView convertRect:caretRect fromView:self.textView];

    CGRect visibleRect = self.tableView.bounds;
    visibleRect.origin.y += self.tableView.contentInset.top;
    visibleRect.size.height -= self.tableView.contentInset.top + self.tableView.contentInset.bottom;

    BOOL res = CGRectContainsRect(visibleRect, caretRect);
    if (!res) {
        caretRect.size.height += 5;
        [self.tableView scrollRectToVisible:caretRect animated:NO];
    }
}
@end

@protocol TextInputTableViewCellDelegate <NSObject>
@optional
- (void)textInputTableViewCellTextWillChange:(TextInputTableViewCell *)cell;
- (void)textInputTableViewCellTextDidChange:(TextInputTableViewCell *)cell;
@end

@interface TextInputTableViewCell : UITableViewCell
@property (nonatomic, weak) id<TextInputTableViewCellDelegate> delegate;
@property (nonatomic, readonly) UITextView *textView;
@property (nonatomic) NSInteger minLines;
@property (nonatomic) CGPoint tableViewContentOffset;
@end


#import "TextInputTableViewCell.h"

@interface TextInputTableViewCell () <UITextViewDelegate> {
    NSLayoutConstraint *_heightConstraint;
}
@property (nonatomic) UITextView *textView;
@end

@implementation TextInputTableViewCell

- (id)initWithStyle:(UITableViewCellStyle)style reuseIdentifier:(NSString *)reuseIdentifier {
    self = [super initWithStyle:style reuseIdentifier:reuseIdentifier];
    if (self) {
        self.selectionStyle = UITableViewCellSelectionStyleNone;
    
        _textView = [UITextView new];
        _textView.translatesAutoresizingMaskIntoConstraints = NO;
        _textView.delegate = self;
        _textView.scrollEnabled = NO;
        _textView.font = CELL_REG_FONT;
        _textView.textContainer.lineFragmentPadding = 0.0;
        _textView.textContainerInset = UIEdgeInsetsZero;
        [self.contentView addSubview:_textView];
    
        [self.contentView addConstraints: [NSLayoutConstraint constraintsWithVisualFormat:@"H:|-[view]-|" options:nil metrics:nil views:@{@"view": _textView}]];
        [self.contentView addConstraints: [NSLayoutConstraint constraintsWithVisualFormat:@"V:|-[view]-|" options:nil metrics:nil views:@{@"view": _textView}]];

        _heightConstraint = [NSLayoutConstraint constraintWithItem: _textView
                         attribute: NSLayoutAttributeHeight
                         relatedBy: NSLayoutRelationGreaterThanOrEqual
                         toItem: nil
                         attribute: NSLayoutAttributeNotAnAttribute
                         multiplier: 0.0
                         constant: (_textView.font.lineHeight + 15)];
        _heightConstraint.priority = UILayoutPriorityRequired - 1;
        [_textView addConstraint:_heightConstraint];
    }
    return self;
}

- (void)prepareForReuse {
    [super prepareForReuse];    
    self.minLines = 1;
}

- (void)setMinLines:(NSInteger)minLines {
    _heightConstraint.constant = minLines * _textView.font.lineHeight + 15;
}

- (BOOL)textView:(UITextView *)textView shouldChangeTextInRange:(NSRange)range replacementText:(NSString *)text {
    if ([self.delegate respondsToSelector:@selector(textInputTableViewCellTextWillChange:)]) {
        [self.delegate textInputTableViewCellTextWillChange:self];
    }
    return YES;
}

- (void)textViewDidChange:(UITextView *)textView {
    if ([self.delegate respondsToSelector:@selector(textInputTableViewCellTextDidChange:)]) {
        [self.delegate textInputTableViewCellTextDidChange:self];
    }
}

@interface SomeTableViewController () <TextInputTableViewCellDelegate>
@end

@implementation SomeTableViewController

. . . . . . . . . . . . . . . . . . . .

- (UITableViewCell *)tableView:(UITableView *)tableView cellForRowAtIndexPath:(NSIndexPath *)indexPath {

    TextInputTableViewCell *cell = [tableView dequeueReusableCellWithIdentifier: TextInputTableViewCellIdentifier forIndexPath:indexPath];
    cell.delegate = self;
    cell.minLines = 3;
    . . . . . . . . . .  
    return cell;
}

- (CGFloat)tableView:(UITableView *)tableView estimatedHeightForRowAtIndexPath:(NSIndexPath *)indexPath {
    return UITableViewAutomaticDimension;
}

- (CGFloat)tableView:(UITableView *)tableView heightForRowAtIndexPath:(NSIndexPath *)indexPath {
    return UITableViewAutomaticDimension;
}

- (void)textInputTableViewCellWillChange:(TextInputTableViewCell *)cell {
    cell.tableViewContentOffset = self.tableView.contentOffset;
}

- (void)textInputTableViewCellTextDidChange:(TextInputTableViewCell *)cell {
    NSIndexPath *indexPath = [self.tableView indexPathForCell:cell];

    [UIView performWithoutAnimation:^{
        [self.tableView moveRowAtIndexPath:indexPath toIndexPath:indexPath];
    }];
    self.tableView.contentOffset = cell.tableViewContentOffset;

    CGRect caretRect = [cell.textView caretRectForPosition:cell.textView.selectedTextRange.start];
    caretRect = [self.tableView convertRect:caretRect fromView:cell.textView];

    CGRect visibleRect = self.tableView.bounds;
    visibleRect.origin.y += self.tableView.contentInset.top;
    visibleRect.size.height -= self.tableView.contentInset.top + self.tableView.contentInset.bottom;
    BOOL res = CGRectContainsRect(visibleRect, caretRect);
    if (!res) {
        caretRect.size.height += 5;
        [self.tableView scrollRectToVisible:caretRect animated:NO];
    }
}
@end

Saving contentOffset before a text change and restoring after the change remove contentOffset jumps on system hyphenation while typing long words.

@protocol TextInputTableViewCellDelegate <NSObject>
@optional
- (void)textInputTableViewCellTextWillChange:(TextInputTableViewCell *)cell;
- (void)textInputTableViewCellTextDidChange:(TextInputTableViewCell *)cell;
@end

@interface TextInputTableViewCell : UITableViewCell
@property (nonatomic, weak) id<TextInputTableViewCellDelegate> delegate;
@property (nonatomic, readonly) UITextView *textView;
@property (nonatomic) NSInteger minLines;
@property (nonatomic) lastRelativeFrameOriginY;
@end


#import "TextInputTableViewCell.h"

@interface TextInputTableViewCell () <UITextViewDelegate> {
    NSLayoutConstraint *_heightConstraint;
}
@property (nonatomic) UITextView *textView;
@end

@implementation TextInputTableViewCell

- (id)initWithStyle:(UITableViewCellStyle)style reuseIdentifier:(NSString *)reuseIdentifier {
    self = [super initWithStyle:style reuseIdentifier:reuseIdentifier];
    if (self) {
        self.selectionStyle = UITableViewCellSelectionStyleNone;
    
        _textView = [UITextView new];
        _textView.translatesAutoresizingMaskIntoConstraints = NO;
        _textView.delegate = self;
        _textView.scrollEnabled = NO;
        _textView.font = CELL_REG_FONT;
        _textView.textContainer.lineFragmentPadding = 0.0;
        _textView.textContainerInset = UIEdgeInsetsZero;
        [self.contentView addSubview:_textView];
    
        [self.contentView addConstraints: [NSLayoutConstraint constraintsWithVisualFormat:@"H:|-[view]-|" options:nil metrics:nil views:@{@"view": _textView}]];
        [self.contentView addConstraints: [NSLayoutConstraint constraintsWithVisualFormat:@"V:|-[view]-|" options:nil metrics:nil views:@{@"view": _textView}]];

        _heightConstraint = [NSLayoutConstraint constraintWithItem: _textView
                         attribute: NSLayoutAttributeHeight
                         relatedBy: NSLayoutRelationGreaterThanOrEqual
                         toItem: nil
                         attribute: NSLayoutAttributeNotAnAttribute
                         multiplier: 0.0
                         constant: (_textView.font.lineHeight + 15)];
        _heightConstraint.priority = UILayoutPriorityRequired - 1;
        [_textView addConstraint:_heightConstraint];
    }
    return self;
}

- (void)prepareForReuse {
    [super prepareForReuse];    
    self.minLines = 1;
}

- (void)setMinLines:(NSInteger)minLines {
    _heightConstraint.constant = minLines * _textView.font.lineHeight + 15;
}

- (BOOL)textView:(UITextView *)textView shouldChangeTextInRange:(NSRange)range replacementText:(NSString *)text {
    if ([self.delegate respondsToSelector:@selector(textInputTableViewCellTextWillChange:)]) {
        [self.delegate textInputTableViewCellTextWillChange:self];
    }
    return YES;
}

- (void)textViewDidChange:(UITextView *)textView {
    if ([self.delegate respondsToSelector:@selector(textInputTableViewCellTextDidChange:)]) {
        [self.delegate textInputTableViewCellTextDidChange:self];
    }
}

@interface SomeTableViewController () <TextInputTableViewCellDelegate>
@end

@implementation SomeTableViewController

. . . . . . . . . . . . . . . . . . . .

- (UITableViewCell *)tableView:(UITableView *)tableView cellForRowAtIndexPath:(NSIndexPath *)indexPath {

    TextInputTableViewCell *cell = [tableView dequeueReusableCellWithIdentifier: TextInputTableViewCellIdentifier forIndexPath:indexPath];
    cell.delegate = self;
    cell.minLines = 3;
    . . . . . . . . . .  
    return cell;
}

- (CGFloat)tableView:(UITableView *)tableView estimatedHeightForRowAtIndexPath:(NSIndexPath *)indexPath {
    return UITableViewAutomaticDimension;
}

- (CGFloat)tableView:(UITableView *)tableView heightForRowAtIndexPath:(NSIndexPath *)indexPath {
    return UITableViewAutomaticDimension;
}

- (void)textInputTableViewCellWillChange:(TextInputTableViewCell *)cell {
    cell.lastRelativeFrameOriginY = cell.frame.origin.y - self.tableView.contentOffset.y;
}

- (void)textInputTableViewCellTextDidChange:(TextInputTableViewCell *)cell {
    NSIndexPath *indexPath = [self.tableView indexPathForCell:cell];

    [UIView performWithoutAnimation:^{
        [self.tableView moveRowAtIndexPath:indexPath toIndexPath:indexPath];
    }]; 

    CGFloat contentOffsetY = cell.frame.origin.y - cell.lastRelativeFrameOriginY;
    self.tableView.contentOffset = CGPointMake(self.tableView.contentOffset.x, contentOffsetY);

    CGRect caretRect = [cell.textView caretRectForPosition:cell.textView.selectedTextRange.start];
    caretRect = [self.tableView convertRect:caretRect fromView:cell.textView];

    CGRect visibleRect = self.tableView.bounds;
    visibleRect.origin.y += self.tableView.contentInset.top;
    visibleRect.size.height -= self.tableView.contentInset.top + self.tableView.contentInset.bottom;
    BOOL res = CGRectContainsRect(visibleRect, caretRect);
    if (!res) {
        caretRect.size.height += 5;
        [self.tableView scrollRectToVisible:caretRect animated:NO];
    }
}
@end

It is important to preserve relativeFrameOriginY (not contentOffsetY!) during cell update because contentSize of the cells before the current cell could be change by autoLayout calculus in unexpected way. It removes visual jumps on system hyphenation while typing long words.