Here's my story for most number of T's.
In 1985 or 1986 (I forget the exact year, but it wa sone of those), my grade school would host a year end tournament for other area CYO 5th/6th grade squads.
During one particular game, a coach tellsa player to go in for somebody and the kid runs right onto the court at that moment. T#1. Coach argues witht he officials about the first T and ends up getting 4 more Ts before the officials let him know if he doesn't leave the gym, the game ends. It's the only time in 21 years I've seen a single coach get 5 Ts and I hope it's the last time.