Which department does a professor in a joint appointment get his/her graduate students from
Both.

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.