First everyone has to accept this is a giant, worthless money pit and any money contributed is a total waste and bad idea. Once that expectation is set then there are few arguments over "ownership", "profit", etc.
Our team shares expenses. We do co-own one car, a BMW project car, but most of our builds have a single owner. It works like this. Someone sees a bad idea on Craigslists and buys it. They ask the team if we want to race their really crappy car. The team cringes and says, "I guess". We then run the numbers on getting it on track; cage, brakes, tires, assorted repairs. I then make a spreadsheet in Google with two kinds of expenses. There are race expenses that occur every time we go to the track like; brakes, tires, and fluids. Then there are durable costs, stuff that should last the life of the car, like; cage, transmission, etc. I usually pro-rate the durable costs over three races. After three races it is paid for and we just budget expenses. In the end team member X owns the car and can sell it whenever. We look at our investment in racing gear as pretty much a loss as a $500 car with a cage is still a $500 car. Anything of value that can be moved, like the seats, harnesses, and fire system, gets taken out for the next car.
Here's an example;
Car prep (cage and needed repairs) = $2500
Race expenses (tires, fluid changes, gas for the tow vehicle, etc) = $1000
Lemons Fee = $1400
*Cost per driver (4 drivers) for the first three races = (1/3 of car prep + Race expenses + Lemons Fee)/4 = $808
*Cost per driver after three races (no more car prep) = (Race expenses + Lemons Fee)/4 = $600
*Note: each driver buys their own jugs of gas for their stint