The University of Southern California (USC) has had the most total NFL draft picks in the history of the NFL.
University of Miami
The University of Southern California with 77 overall first round draft picks as of the 2012 draft.
The University of Texas with 17 in the 1984 draft.
University of Southern California
In theory, an unlimited amount, but 13- 15 picks is usually the most.
auburn, nd and usc tied with 5
kentucky in 2012 had 6 of their players chosen in the draft
Auburn, Notre Dame, and Southern California (USC) all have 5
ThE University of Kentucky
Kentucky, 2010, five first round picks
The USC Trojans.
Not sure if it transfers into real life, but in madden 2011 (Which is has been very accurate on the rules of the NFL) the maximum number of draft pick one team can have is 9.
College of the Holy Cross