Some universities do not clearly state that I should not or must not contact potential PhD advisors. For instance, one says it is not "necessary" to contact an advisor during the application process. Supervision will be decided later. Does this mean contact is not necessary but you can do it if you like? Or does it mean not necessary so do not attempt at all?
(I am applying to do a PhD in educational sciences).
Actually, the instructions are SUPER clear.
With these instructions, I would recommend only contacting a professor in that department if there is a real reason why you feel that a professor might choose to advocate for you in the admissions process. You should consider this a substantially high bar to get over.
For example, if you've met the professor at a conference because of research you've done, or if you've been very immersed in research directly related to that investigators lab. In this case, you're probably doing the professor a favor by pointing out that there may be an entering grad student they'd have interest in.
An additional time when I think it would be a good idea to contact the prof is if you would only attend that university if offered a slot in that professor's lab. In this case, contacting the prof to find out if this is a viable possibility can save both you and the program you're applying to time and expense. If there are three or four labs you'd be willing to work in, skip this.
Generally, at least in the US, it's probably only a good idea to contact the prof if establishing a relationship would be mutually beneficial, keeping in mind that the prof will be competing with other profs for the best grad students in their program.
If your letter to the prof would look like "you don't know me, but I've heard of your field and I think I would like working in it -- please do what you can to get me admitted" -- that's pretty much just noise.
My advice is that you don't contact individual professors unless it is clearly required, as is true in some countries and in some field more generally.
In particular, don't flood them with the things that would normally appear in an application sent to the department/committee. They have no need to see this and are unlikely to do anything more than delete what you send. The more courteous will send you a note to apply through channels, even if they don't actually look at what you send.
People are busy. Don't ask them for things they probably can't do and that would interrupt their work process. And don't try to circumvent the normal application process. Nobody will be impressed by that.
On rare occasions, it is possible that one professor will recommend a student, out of process, to a colleague at another university, but only if some special circumstance applies that the sender thinks the receiver needs to be aware of. I have done this, successfully, though it was part of the application process, when it was clear that something in the record was misinterpreted. But a student has no "standing" to do this on their own. And, I was putting my own reputation on the line, of course.
