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But sorcerers present a problem. They both challenge the guild structure of the wizards and they are unregistered and therefore uncontrolled (to an extent) magic users. So... logically, the universities would want to kill or neutralize them. Which seems a level of evil I'm not sure I want the world to have, but maybe it could work? (The more I type, the more I think maybe I should make the universities like the Catholic Church under the Borgias- super corrupt, s!~@ty, and decadent. Hell, wizards could be in a place where they are supposed to be celibate so they don't make any sorcerers)
The universities detect uncontrolled magic and take in all children who manifest sorcery, training them to be wizards, or at least adepts. You might have an unusual percentage of NPC magic-users with INT 11, CHA 13, or a couple of campaign traits that give effectively half a sorcerer level (either a spontaneous spell or a bloodline power).