Of my point of you, the major benefit of partial classes is to separated automatically generated code (e.g. by designer) from the code written by the developer, you can let the tool to regenerate the code without any fear of losing your own coding.

Spliting the source to parts maintained independly by several developers doesn't soud good, because it indicates bad design. Having classes so huge that many guys can work on them together is not good idea, I'd said.