An article in the Daily Mail bemoans a pundit's musings about billionaires owning land on the moon.
Until 1860, the flag of the British Hudson Bay Company flew at Fort Vancouver, 12 miles north of my 1960-built house. Britain, a nation full of brilliant people, which once claimed Oregon, owned the eastern United States, Ireland, India, Palestine, Egypt, Hong Kong, and other bits of real estate on which the sun never set, nonetheless has had trouble retaining both billionaires and offshore acreage.
So ... the opinions of British off-brand tabloids in matters of off-earth ownership are disputable.
As someone living on ground formerly used by the Chinook tribe, on the border with the Clatskanie and Kalapuya, I've noticed that land is owned by members of the most powerful gang. My mortgage is indirectly owned by the Chinese, who have been nice about not repossessing it (so far). Lawyers can argue about who owns what, but the first to grab and hold the land against all comers, prevails - until a bigger army comes along.
That said, "land" is an outdated concept. Farmers are poor, Monsanto is rich. Bits trump atoms, and productivity outperforms place. That is why the Chinese own my mortgage, not vice versa. When we pull our heads out of Hollywood's anus, and start thinking with them again, this will change. Geopolitics is about mobility, not acreage. Projecting 19th century values into the 21st century is misleading.
In space, a few tiny lumps of rock are almost irrelevant compared to energy and orbits. The sun produces 380 trillion terawatts. The Earth intercepts 170,000 terawatts, the moon intercepts 13,000 terawatts. All the other planets intercept 13 times as much, totalling a tiny 4.2 parts per billion of total solar output. The really interesting claims will be on the other 99.9999996% of the sun's energy output, and the orbits of the machines that use it.
I don't need the moon, or any particular body, to build orbiting machines. Though convenient, the moon is not essential. The inverted pyramid of rock, magma, and molten iron under "my" 0.65 acres of land weighs 1.2E14 kilograms, with a delta-V from depths to earth orbit lower than the delta-V from any asteroid. "My" mass could be spread into a molecular-engineered foil intercepting a million terawatts, more than the Earth, half as much as all the planets combined. I would rather leave my garden intact, and buy mass from your wedge. Or your tailpipe emissions; you discard all that yummy carbon, I'll take it!
Planets and other orbiting objects are mostly collision hazards and orbit perturbers. We don't need much of them to build a solar system economy.
Orbits are what really matter. Property rights in space will be an evolution of navigation and derelict hazard rights. There are ways to map orbits onto a torus, nest the torii, and fill space with huge numbers of non-intersecting orbits, with millions of objects sequenced along those orbits. Light pressure and multi-body gravitation perturb those orbits, expanding the easements around orbital properties. There remains a LOT of cubic out there.
Leaving an assigned orbit and colliding with an object in another assigned orbit will be grounds for a lawsuit. "Property" is about who gets to sue whom when collisions occur; it is "my lane" if you hit my car while changing lanes, and your insurance company that pays. Unless it is my planeload of haji pilgrims versus your global navy, in which case See figure 1.
The planets may function as benchmarks for orbital property. When someone changes a planet's orbit by launching enormous quantities of mass from it, that may lead to legal wrangling as we recalculate the resulting orbits. Rearranging the mass on the surface won't matter much, the center of mass does not move, and hydrostatic equilibrium will restore the small harmonic components of the gravity field.
If there are billionaires silly enough to blow their fortunes on deeds for lunar surface (issued by what authority, backed by what military force?) let them. If one of them charges too much for regolith, I'll buy from a different silly billionaire. Or just take it and ignore their complaints - that's what we did to the Chinook tribe. There is plenty of usable mass down here and out there, nobody can corner the market. The trick is to use mass sparingly, and use energy abundantly, transforming it into high value products like carefully crafted gigabits.
In the information age, the only valuable item is intelligent attention. A billionaire has no more of that than I do.