Changing supervisors in graduate program
The idea of a graduate (or PhD) program is to form the student into an independent researcher. This normally includes the liberty of the student to choose his own projects and research. On the other hand, the student also has to learn about funding, e.g. it might be that he only gets money if he works in As lab at least XX hours a week. This also counts as learning experience: If the student wants to work elsewhere, he might need to acquire new funds for it.

Regarding your question what of it is standard or not, that highly depends on field, country, university, even institution. Thus it would be best to ask your advisor, other students,... about how it is handled.