Seems like half of the top Genovese guys used to/ are jersey boys.
Yes, at one time they probably had close to a 1/3 of their official membership in NJ. Aside from the DeCavalcante's, IMO the Genovese had the closest thing to a resident sitting borgata based in NJ as well.
Many of their bosses, past and present were Jersey based, as well as top skippers. They always had 4-5 crews there as well. Big presence!