The person who signs the ticket can then arrange for the winnings to be disbursed as he/she sees fit. Usually when multiple owners are involved (such as an office pool), they hire a lawyer. The lawyer than claims the ticket and divvies up the winnings (after taking his cut, of course). All of this is drawn up legally ahead of time.
But it is never a good idea to participate in such a pool because there are invariably hard feelings. I can't remember all the details but there was an office pool a few years back that won a multi-million dollar prize. It got real nasty because the group tried cutting out a couple of members who didn't pony up the money that particular week. As well, other co-workers who weren't in the pool tried to claim that they were and so forth. It got ugly.
A group of people in Westerville (Columbus), OH won a powerball lotto (they went cross state). They all were able to divy it up just fine and one family moved just a few houses down the road from us. They were rednecks who moved into a beautiful white house with a pond. They played bluegrass and waylon Jennings on the weekends outside during the summer. Pretty funny folks.