In January of 2024, the company Astrobiotic was set to make history with the first privately-developed lander, named Peregrine, to reach the lunar surface, sent aboard a United Launch Alliance's Vulcan Centaur rocket. The lander carried the usual sorts of scientific instruments, many of them developed by NASA and its research partners. But tucked away among all those instruments was a small payload, with spots in that cargo sold by the companies Celestis and Elysium Space.
If not full ownership, eventually groups of people will have to have some sort of jurisdiction over certain regions on the moon.
Can we divide it up into sections like we have with Antarctica?
The states that have claims over Antarctica exercise no effective jurisdiction over them. The Antarctic Treaty basically just confirms their existence, gives the US and USSR the right to each make one whenever they want, and then moves on to laying out what can and can’t be done on the continent without regard to the claims.