The University of Southern California with 77 overall first round draft picks as of the 2012 draft.
Kentucky, 2010, five first round picks
if your talking fir round picks then the green bay pakckers since they are the oldest, but if your talking first overall then the baltimore/indianapolis colts hold that title
Illinois
In theory, an unlimited amount, but 13- 15 picks is usually the most.
Duke University has one of the richest basketball traditions in the United States. To date, Duke has had 35 first round NBA draft picks. The first came in 1963 and the most recent came in 2014.
NFL teams typically have a total of 7 picks in the NFL draft, one pick per round. Teams can add to their total number of draft picks by trading players for future draft picks or trading a singular high draft pick for multiple lower round picks. In addition teams can get what are called compensatory picks, which are given out to teams if they lose high quality players to other teams during free agency. These compensatory picks cannot be traded to other teams.
The University of Southern California (USC) has had the most total NFL draft picks in the history of the NFL.
The University of Kentucky in 2012 placed a total of six players in the NBA, five in the first round and 1 in the second round. This included the first time ever for the first and second draft picks from a single University.
Orlando magic
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Texans