Is this behavior not natural? I could see a fight where fatal wounds would occur, but by nature is a dog in a fight set out to kill the other dog, or are they just trying to establish dominance and run off the other dog.

It depends.  Normal wild dogs all have jobs in the pack and depend upon each other for survival so serious traumatic injuries are rare and not normally intended.    With the domestication of the dog this has been lost and bred away from some of the dogs.   So a fight to the death can happen.

Often dogs in a fight will experience an endorphin rush instead of pain providing a negative feed back it triggers more and more aggression and a desire to stay in the fight.

Write Michael Vick a letter and ask him. I'm sure he is awefully bored.

Ummm no.

Dogs that are retardedly feral, yes.

Dogs that are aggressive and not stable get driven OUT of the pack.

The most aggressive dog is never the leader, it's usually the first one to get kick out or ganged up on by the other dogs.

The leaders of the pack are always the most stable.