When a department enrolls x number of students based on the capacity of the department and its professors, the ideal desire is fair distribution of PhD students among faculty members. However, students are attracted to attractive professors (by different factors such as fame, personality, etc), and there should be less or no request for some faculty members.
Assuming a student and advisor mutually agree that they would like to work together, but the department would rather have the student work with another faculty member who is short on PhD students. Can the department limit the number of students that may work with each faculty member, so that new PhD students will be distributed among faculty?
In a hypothetical situation, there are 10 PhD students, and 10 faculty members. Can the department set the limit of one PhD student per faculty to ideally distribute the students among faculty members?
Note: This question is not about the cases in which a candidate specifically apply for working under supervision of a specific professor (due to the admission system or funding source).