Who decides about admission of a PhD student?
Let me explain my comment as an answer.

The admission process works in two different ways: Formal enrolment and informal enrolment

Formal

You apply through university web link and select the research areas or supervisor. Then probably you communicate with the chosen supervisor through email(s). If things go well then you might get an interview call or direct admit.

Informal

You approach the supervisor first. Discussions or interviews may go on. If everything is alright, you supervisor would speak with the admission committee for your official admit.

In both these types of cases your supervisor recommends for the admission. However, it is the decision of the admission committee to make the final call.


  Note: I have skipped the recommendation letters related points which is a major part in both these types of enrolment.


Moreover, each University has their own set of rules. It is wise to go through the same.