Trafficante did in fact have the strongest ties to Cuba other than perhaps Lansky. As I understand it, Trafficante controlled the gambling on the whole Gulf Coast of the United States and Marcello had the land going as far as Dallas, Texas, where the Civello family operated under his flag. They both had 20-50 men but still had so much reach it's incredible.

I put Buffalo as second tier because their membership was always the highest behind the new york families and Chicago depending on how you count it.