Elsewhere in this thread I posted references (but not links) to the Soviet experiments (first of keeping a severed dog’s head alive on artificial heart and lungs, then of grafting one dog’s head and paw to another living dog, both breathing and eating from the same dog’s throat, lungs, heart).
I saw that and I can see how such a thing could be done with surgery where the blood supply is carefully spliced together. In the case of the musician’s finger, though, his body had to reconnect the blood supply spontaneously. That is pretty amazing.
Regarding reconnecting nerves, it looks like nerves in the peripheral nervous system can reconnect and heal back together so that their function is restored. The best outcomes are in the young and when the nerve is cut cleanly. It’s the central nervous system where regeneration is not possible.
http://en.m.wikipedia.org/wiki/Neuroregeneration