The Hubble picture of ARP 194 made me wonder about what actually happens when galaxies collide, merge or what would the best word be? We've seen them seemingly pass through each other, being left with much distortion. And I've read that collisions of stars would be rare, because there are still light years of empty space between them. But statistically, billions of stars within dozens of light years ought to yield quite a few collisions. Do we have any idea how many, or what actually happens when stars collide?

(Let's assume for now that the black holes go their own ways.)