According to some theories I`ve read and heard, when 2 black holes fly to each other (with whatever mass, diameter, radius, speed etc...)they do not do what you wrote above because according to Einstein nothing can go faster than light. What they do instead is the same as when 2 tornados come too close to each other, they meld together, thus when 2 black holes caome together, they meld and every characteristic of both of them goes times 2 (mass of BH1 + mass of BH2, size of BH1 + size of Bh2, etc..)