First, you and other stakeholders have to decide at which level of granularity you want to apply the use case technique. Usually, it is applied to the system "as a whole" only and other specification techniques are used to specify the behavior of components. This is what I would recommend.
Apparently, you have made the unusual decision to apply the use case technique to components as well. In that case, I would strictly separate the use cases of every component, i.e. every component would get its own use case diagram. In such a diagram, the components it interacts with are actors.
If component X gets input from actor A1, processes it and sends the result to actor A2, I would define one use case connected to both A1 and A2. Do not separate 'receive', 'process' and 'send' in separate use cases. Instead, these are three steps in one use case. If this is complex behavior, you may draw an activity diagram or state machine diagram to describe the internals of the use case.
For those who are able to read Dutch, I have written a short article on this subject: Service model en use case model : een lastige combinatie.
Figure 18.11 of the UML specification shows that use cases may be organized in packages. In this diagram, the system border is not displayed. All use cases apply to one system, called ATMSystem (as displayed in figure 18.10 of the UML spec). Within this system, multiple packages are defined. Defining packages is especially useful if you have a lot of use cases and you want to organize them in logical groups, which may or may not be reflected in physical entities, like software components or Java packages. In figure 18.11, use cases that are displayed inside a package symbol, but do not belong to that package, are shown in grey. They are displayed inside the package symbol because they are referred to by use cases that do belong to the package.