Partial and abstract classes

Methods or properties of an abstract class which are themselves marked abstract must be overridden in a child class, unless the child class is itself abstract.

Notice though that not all methods or properties of an abstract class need be abstract and static members are never abstract. 

The reason for using partial classes in the first place is to split the class over two (or more) source code files so different programmers can work on different parts of the class at the same time.

This is particularly useful when a code generator is generating code for part of the class such as when creating a Form class in Visual Studio.

In the case of an abstract class, I'd have thought it was unlikely that a code generator would be creating part of the class but two or more human programmers might want to work on it simultaneously.

Incidentally, you don't necessarily have to declare all the partial classes as being abstract. If just one is abstract, then so is the whole class.