[Mediterraneo10]

The amount of possible PhD positions in a department is limited by the number of faculty, because each student needs a supervisor. A supervisor can only supervise so many students at once before he or she feels overworked, and each PhD student to supervise may distract from that scholar's own research.

[marceloabsousa]

Sure it's a finite number but it's not uncommon for a faculty member to have 5+ PhD students. It all depends on the number of post-docs or senior PhDs they have in the group. The major limiting factor is really money - if a faculty member gets a $5M grant, they will hire as many PhDs as they want or even get some faculty hire for the project.