Not a divorce, but maybe they could live separately.
What would be lost if UNC basketball was divested into an LLC? It would retain all the intellectual property -- i.e. uniforms, logos, history -- and facilities (lease or ownership, I don't know), but the players wouldn't have to be students.
I submit nothing would be lost. I asked this question before and people said that it was important to them that the players be students, but it seems that's more or less water under the bridge. I mean, players might attend classes and all, but if you transfer three times in four years, you're not really much of a student. And it's been a while since I've heard of a player being academically ineligible.