It depends on what you use for the selector. Major College/D1A/FBS teams have never had an official National Champion. (assuming you mean the before mentioned divisions). See the related link below.
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In Football it is Princeton with 28 titles. In Basketball it is UCLA with 11 titles.
116 national championships since 1895 in football. However most teams don't count their national championship pre ww2!
Paul "Bear" Bryant for Alabama.
cristiano ronaldo
University of North Carolina at Chapel Hill