Who dominates the ACC outside football and basketball? Posted Aug 23, 2019 North Carolina runs not just the ACC but also the women's college soccer world. The Tar Heels own by far the most national titles in the sport, with 21. Carolina also has dominated field hockey. The Tar Heels have seven national titles and 21 ACC championships and won the title last season. UNC has 11 individual swimming & diving national champions. (ESPN.com)