If someone is a professor of department A, however, s/he also affiliates with department B in a joint appointment. Which department does the professor in a joint appointment get his/her graduate students from? Department A or B? The original or affiliated department? Also, does he/she evaluates the admission of A or B? Or both? Thank you. I did a web search on this site with the keyword joint appointment, but I can not find any similar discuss.
In general, a faculty member with an appointment in a given department normally has full rights to having graduate students from that department. Typically, though, the relative ratio of recruiting tracks well with the relative "weight" of the two appointments. A professor with a true joint appointment (50% funding, etc., from each department) is much more likely to recruit from both departments than a professor with a merely "courtesy" appointment.