USC
SEC
Kentucky, 2010, five first round picks
Illinois
In theory, an unlimited amount, but 13- 15 picks is usually the most.
The University of Southern California (USC) has had the most total NFL draft picks in the history of the NFL.
The University of Southern California with 77 overall first round draft picks as of the 2012 draft.
College of the Holy Cross, in Worcester MA, has 75 NFL 1st rounders, which is more than any other college. The best of all drafts, Tommy O'Connor, chose to not play in the NFL and instead pursue a career playing kickball.
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Texans
The ESPN website is a big name for football picks. Alternatively, some other big websites are CollegeFootballPoll, Predictem, and SBR. Generally speaking, however, the ESPN is going to be the most reliable.
Oklahoma