Suppose that a student joins a graduate program with supervisor A. The supervisor has a bad reputation in the research group with a history of not caring for his students, e.g. professor goes to sabbatical on a regular basis and does not skype with his students, replies to emails from students in 5 minutes, does not help students with their coursework, expects students to comment on his research work, expects students to be independent, etc.
Incidentally, after a few months, he becomes more interested in the research interests of supervisor B in the same research group.
In this case, it is standard procedure for the student to be officially co-supervised by both supervisors A and B even though the student's projects are all supervised by supervisor B.
Now consider an alternative scenario. The student becomes more interested in the research interests of supervisors B and C.
In this case, is it standard procedure for the student to be officially co-supervised by supervisors B and C? In other words, does the student leave supervisor A completely?
How common is the second scenario in graduate programs?
Does the switch leave a bad impression of professors (in the research group) on the student?