Personally I fit all of my classes into one Class Diagram without much of a problem. It was a pain to get all the lines to look nice without crossover though
. I started out with three separate Class Diagrams and then consolidated them at the end.
As far as the difference between Class and Component Diagrams, there is difinitely a significant one. Think coarse-grain for the Component Diagram and fine-grain for the Class Diagram, so your helper and miscellaneous classes will not be part of the Component Diagram. The Component Diagram is also where you get a chance to illustrate the separate servers where all of the components reside.