When assigning A=B, does this call A's or B's assignment operator?

If I have two classes A and B and I do A=B which assignment constructor is called? The one from class A or the one from class B?

There's copy constructor and there's assignment operator. Since A != B, the copy assignment operator will be called.

Short answer: operator = from class A, since you're assigning to class A.

Long answer:

A=B will not work, since A and B are class types.

You probably mean:

A a;
B b;
a = b;

In which case, operator = for class A will be called.

class A
{
/*...*/
   A& operator = (const B& b);
};

The conversion constructor will be called for the following case:

B b;
A a(b);

//or

B b;
A a = b; //note that conversion constructor will be called here

where A is defined as:

class A
{
/*...*/
    A(const B& b); //conversion constructor
};

Note that this introduces implicit casting between B and A. If you don't want that, you can declare the conversion constructor as explicit.