What happens when two black holes hit each other? would the bigger one manage to pull matter out of the smaller one from a distance, until what’s left in the smaller one wasn’t enough to stay a black hole, so half of it explodes away from the big one? Do they maintain integrity until they actually overlap, become one? Just get bigger and blacker?
Yep.
The two black holes merge into one bigger black hole.
The LIGO observatory claims to have detected a number of black hole and black hole- neutron star mergers.