Do all professors have to have at least 1 grad student?

[gliter250]

I applied to work with a professor who typically takes on 1 or 2 students at a time. His current and only student graduates this semester and I was the only one invited to come interview to work with him. Do professors without students get "dibs" over professors who take on 2 or 3 students? Also, does this increase my chances of getting into the program so that the professor isn't left without a grad student?

[fuzzylogician]

The answer to all/always questions is almost invariably 'it depends,' because there are going to be outliers and exceptions. The question is how likely those are going to be in your situation. The way admissions decisions are made varies greatly. In some cases, the department as a whole admits students, in others each professor takes whoever she wants to work in her group and doesn't need to consult with anyone, and of course there are all kinds of setups in between. It's entirely possible that some faculty members are more politically powerful than others and get to influence these decisions, but of course we can't know if that holds in your case. 

For an active professor who usually takes on a few students at a time (a year? it'd be on the low side if he only had 1-2 students in general), I'd imagine he'd be looking to replace the students who are graduating. On the other hand, if the professor used to have lots of students and he just phased out his last remaining one, that sort of sounds more like he's in some kind of process of vamping down, be it for a sabbatical, because he is moving to a new job, retiring, lost funding, etc. Then again, you're being interviewed, so maybe there is no mystery and it just so happened that it's a slow time for this professor. It's really hard to know. I'd guess that assuming that he is staying there and is an active researcher (=not retiring or anything), there's a good chance that he'll be looking to take on a new student, and if you're the only one being interviewed, then your chances sound pretty good. Obviously, no one can make you any promises. But you should go in assuming that it'll work out and give it your best shot. You never know what other considerations might be at play behind the scenes and it's just not worth worrying about it, since it's completely outside of your control. 

[gliter250]

That makes sense. Thank you! I did have a great connection with him when we originally spoke so I will worry a bit less.