I am presently a third year graduate student. I am currently being supervised by professor A. Recently, I am co-supervised by professor A and B. Now professor A decides to leave, and if I graduate in two years, who will be my final advisor? A or B or A and B?
I've been in this situation as Professor A. One student moved with me to location U. One stayed a student of location K but spent a lot of time in location U. The other stayed in location K. I still supervised him, but he worked a lot more extensively with Professor B.
U and K are in different countries, but K kept me on in a 10% appointment so that this would work administratively.
I told the students I was leaving and gave them all possible options I could cater for – unfortunately, I could only pay for one of them at location U. For various reasons, students took an option that suited them.
Before you discuss it with Professor A, you need to think about what you want, assuming that following Professor A is an option. And think about how well you would work with Professor B, if you cannot follow Professor A. The last thing you want to do is be left without adequate supervision.