I mentioned this before but nobody seemed to notice. Does my idea about "3 nautical miles out = outside the jurisdiction of any state" actually work? Or would it immediately become part of the state, and if so, would making it a ship or huge raft rather than an island prevent such from happening? I know we have a few lawyers on this forum.
This is a complicated question.
The United Nations Convention on the Law of the Sea (UNCLOS) allows territorial claims within 12 NM (about 22 km or 14 miles) from the coastline. The coastline itself can be tough to determine, especially in those areas with significant tidal variations. There is also a thing called archipelagic waters where a baseline can be drawn between two coastal points and territorial waters being anything inside that line; Qaddafi did this back in the day to claim the entire Gulf of Sidra
which didn't work out too well for him. There are also the 200 NM Exclusive Economic Zones (EEZ) and special continental shelf rules which can extend a country's influence far beyond the 200 NM EEZ.
Chances are that any new island will be difficult to build outside of all the above zones. You'd need to find a shallow enough area of the sea that is outside all claims as any attempt to build an island will probably fall within some country's EEZ
and continental shelf claims. (If you build inside the EEZ, the country can claim your entire island as a resource. It could also probably then extend its EEZ using your island.) Next, you'd also have to guard/man it constantly while building to avoid any person or country claiming it as their own. There may be other problems, but I only know of the UNCLOS issues since it was something
my old office frequently dealt with.
It should be noted that the US has not ratified the UNCLOS but general follows the rules.