Disclaimer: I am not a pilot, nor an airplane owner. Just someone that wants to be all of the above.
My impression is that the details of this sort of thing are whatever the owners decide it to be. You and your fellow pilots work out the costs of ownership and usage (monthly payment to the bank, fuel, insurance, maintenance, annual inspections, overhaul, hangar space, yada, yada) and decide what you think is a fair way to divide it up. Maybe each contributes $X to pay insurance, hangar and payment, whether you fly or not. Then every hour of flying costs $Y, which goes towards maintenance, something for the eventual overhaul, annual inspections and so on. Maybe if it’s getting used enough, you pay $Y+ per hour, and that covers all of the above.
The same goes for scheduling. You decide - Does Joe get the bird on the 1st weekend of the month, and Mary the 2nd? Does it go to the first one to reserve it? What if someone wants it for a long holiday weekend, but that’s Fred’s time? You as a fractional owner have to work it out.
Speaking from no personal experience whatsoever, if I was in such a group, I would want a president, or manager, or whatever you want to label them, as being the person who schedules maintenance, oversees the fund, etc. This would be an experienced person who knows what is involved with owning a plane, IMHO. Maybe such responsibility would allow extra flying time for just the cost of fuel, or first choice for primo weekends (Fun 'n Sun or Oshkosh come to mind…) Oh, and I’d want this all down on paper, including how you bring a new owner on board, how one sells his share, what minimum training or licensing is required of each owner, etc. I see a lawyer involved in all of this, I think.