Hawaii (the mouse that's roaring among the above lions) has two divisions (1 and 2), roughly based on size of school. Oahu has a public and private league in each division, the other island leagues (Kauai; Maui/Molokai/Lanai; and the Big Island) include both public and private schools. Both public and private schools compete in the state tournament.
Prior to 2011, private schools dominated states but since then, public schools have won 7 of 10 D1 state titles (2 from Oahu, 2 from the Big Island, and 3 from Maui).
Both tournaments are single elim.
D1 Tournament
Oahu public: 5 schools
Oahu private: 3 schools
Maui: 2 schools
Big Island: 2 schools
D2 Tournament
Oahu public: 3 schools
Oahu private: 1 school
Maui: 1 school
Big Island: 2 schools
Kauai: 1 school