In our group the guy that puts the first hit on it gets the deer and really regardless of that hit. We all share the workload and help each other out, it all works very well and equal in the end. I am just as happy gutting a partners animals as if I were my own and visa v.
However I assume your talking about different hunting parties, then I'd lean towards the first vital hit gets the animal...but how does one determine this for sure without going CSI! Most likely the hunter who gets to the animal first will win the right wether warranted ot not. I am glad this isn't an issue for my areas and if it were I certainly wouldn't claim or shoot another hunters animal, if I did and he established it was wounded when I fired than I wouldn't argue, most likely ask him if he needs a hand(either dragging or at the range

). Why fight over a dead animal when many others are still on the hoof? Arguing would just waste time, effort and energy - most likely not resulting in a very good feeling regardless of the outcome. If the killing is your only reason than quite simply your are missing a boatlaod when it comes to hunting! It is reward that isn't required in my mind to thoroughly enjoy myself. However being in a company of a$$hole$ who would, I'd hit the dusty trial for greener pastures very quickly as this wouldn't make me feel very satisfied!