Some questions before said that in US/Canada, we should apply first then select the professor and it's different from the system in UK or EU. So, what about Australia or New Zealand?
From my experience in Australia, the usual scenario is that a student makes contact with a particular academic at a university. The academic agrees to supervise the student's PhD. The applicant then applies through the official university process. The university process will involve additional hurdles (e.g., grades, English language requirements, past experience writing research theses, etc.). But in general, the applicant starts by building a relationship with a potential supervisor.
That said, some applicants get in contact with the university with an outline of their research interests, and then the university can facilitate finding a supervisor.
And of course, I'm sure there is some variability in the process across universities. So of course, it makes sense to check out the university websites and get in touch with the HDR office of any relevant universities.
The usual practice in New Zealand is that PhD admissions are formally carried out at the university level and not by individual staff or even individual departments. It is common to be in contact with prospective supervisors in advance of applying, and sometimes required, but they usually cannot actually accept a student entirely of their own choice. It is, however, required that there be a willing supervisor before a student is accepted.
A student can begin the process without a supervisor arranged, and the relevant department might find and assign one. Whether that happens before or after the formal application varies, but the effect is generally that the student will be interviewed by one or more of the prospective supervisors before an admission decision is made:
- At my institution, the application form asks for the names of any staff you've been in contact with, and if you leave that blank the departmental committee enquires with staff who seem relevant about whether they'd like to follow up.
- At others, you enquire informally with the university and they collate information to send on to the department, and only afterwards do you apply.
In either case, forming an existing connection with a willing prospective supervisor before applying means that's likely to be your supervisor if you're accepted.
Funding decisions are usually made by layers of committee, in parallel or separately to the acceptance process. In the (less common) case of grant-funded PhD studentships that can be sidestepped and the supervisor has more sway.
An accepted student will usually be assigned a primary supervisor from the start, but sometimes there may be a brief initial period where that is uncertain. It is possible to change supervisor after starting, but it's not usual that there's an unsupervised period after arrival where you're meant to find a supervisor like there is in some places.