I'm very interested in working with a specific professor, who is a full-time full professor in one department, and adjunct faculty in another. In this case he is not a part-time adjunct who only teaches. I'm more interested in being a grad student in the second department, for a number of reasons that aren't important to go into.
In the US, would it be typical for such a professor to be able to supervise a grad student in the second department? Or is this likely to vary by school? The department website is unclear.
I know I can ask him, but I thought this would be a valuable question for the community as well.