 What college basketball teams have had the most first-round draft picks? What school? All-time? All-time. Well, I would say, how many schools are we talking about? All of them. I mean, who do you think? I mean, UCLA would obviously be one. North Carolina? North Carolina's in the top three. UCLA's not in the top three? Not in the top three. So first-round draft picks. Okay, North Carolina, Kentucky.