JAK+ are allowed to take on official padawans. There is no maximum amount of padawans a Knight (or above) may have; however, most JAK+ do not wish to take on too many padawans. By having a master, one can attend padawan sessions, get 1 on 1 training from one's master, and have a role-model to look up to. Some students, who usually can't or don't attend classes, are inclined to look for a master to train them on their own time.
Jedi Academy Students can have "training partners" (commonly called padawans) aswell, but they will not be official.