It is the mage who chooses his students and apprentices. It is never the other way around.

The only analogy I can think of is a modern dance or a theater company. It is the artistic director who chooses who become the members of his ensemble.

In the case of the modern dance company, the artistic director chooses members who have a specific "look", as with the Alvin Ailey American Dance Theater.

In the case of the theater company, the artistic director chooses members who can fit into "character types" capable of performing roles in a repertoire, as with the Moscow Art Theatre.

I have my own criteria, and I immediately reject "applicants" I do not wish to waste my time, intelligence, and resources on.