Bsrgvty

Firstly, I am not specifically talking about PhD supervision. I think that's less relevant for my question since a PhD supervision is usually a mutually beneficial arrangement, as the professor gains a PhD student to help them with related research.

My focus is more on supervision of bachelor and masters theses. In these, there is less benefit to the professor to act in a supervisory role.

So with that in mind, if a student contacts a professor because they need a supervisor for their bachelor or thesis project (something which is a requirement in order to get the degree), is the supervisor obligated to accept this role?

I don't think the answer is yes, since people usually say that if you want to get a supervisor, you should ask your professior if he/she wants to. So the words imply that the professor has a choice and could turn you down.

And so if the answer is indeed no, how does the system then work? What happens if nobody wants to supervise one particular student? Is that student then just screwed?

The exact answer to this is likely to vary from one university to the next, depending on local rules and terms of employment. In general, the position is likely to be: professors are not required to agree to a student's request for supervision. However, it is generally advisable/mandatory for professors to accede to 'requests' that come from higher up in the management hierarchy.

If students are required to complete a supervised project as part of a course, then it is the university's responsibility to ensure that an appropriate supervisor is made available. If a student reported that they cannot find a willing supervisor, this would likely result in management applying increasing amounts of pressure and/or incentives until someone agreed. However, in such circumstances, the student is likely to be left with Hobson's choice - the project offered may not be a close match to the student's preferences.

There is lurking here a possible problem for departments. I am talking about US universities.

Of course the professor is rewarded for advising students, perhaps merely as one of many considerations for promotion and raises.

But it could be a problem if that reward to the professor is more when the student does great work and less when the student does average work. That arrangement will encourage professors to decline the weaker students. I have advised students of both types; the work for me was much more when the student was weak.

If a department wants to be friendly to students of all types, it should take care to fairly reward professors who take on weak students.

Professors mostly have a choice. Especially concerning individual students. Students shouldn't really want to be mentored by someone that doesn't want to mentor them.

Of course, department policies may intervene, either explicitly or implicitly. In the long run, a professor who refuses to mentor any students is likely to get some pressure from the department for not doing their part. Some professors provide their department excess value in other ways and might get away with doing less. For earlier-career professors, supervising theses can contribute to tenure or promotion.

I'd also challenge the idea that only PhD students can do something productive for a professor, though: the junior students might need more direction but can still do good work.

Especially if a thesis is a degree requirement, I would expect the department or program to ensure something can be done to get a student some sort of supervisor, but it may not be their first choice and they may not be able to choose their project. I'd expect the students who are most stubborn about their interests or are otherwise difficult to work with would be most likely to run into problems.

For research students, that is, PhD and research master's, professors almost always have a choice naturally (excluding rare informal pressure made on them due to unforeseen circumstances).

For taught master's degrees, as well as bachelor's thesis, professors mostly do not have much choice to supervise pre-allocated students, because if a student already was accepted to study in the department the student must complete such a dissertation in their final year. However, the way that such mandatory taught supervision tasks are allocated to professors varies from place to place.

For a bachelor student actually suggesting to a specific professor to become their supervisor, most chances is that the professor has a choice to decline because this was an initiative of the student, and not part of an administrative scheme made by the department to allocate students to professors.

Of course, this varies from university to university, countries, continents etc.