Who would own artificially created real estate?

[Destructionator XV]

I am in the middle of another post in my blog, and I encountered a question that I am not sure what the answer is.

Suppose some real estate can be artificially produced, like a space colony, but this would count for an artificial island in international waters too. Then suppose an international company decides to build one of these islands / colonies itself. Under what government would the island fall?

The answer is reasonably easy if it is in the national waters (or space) of a nation, as then it would be just like building a structure on land. You might privately own it, but you are still subject to that country's laws. But in international waters or space, no such simple claim can be made.

My first thought might be it would be under the laws of the company's country of origin, which is why I specified an international company: it doesn't really fall under any one government, especially if operating on a wholly artificial structure they build in unclaimed waters.

So what would happen to this island / colony? Would it be the domain of the company to do with as they please, with no government oversight? This seems like a bad idea to me (though could realistically lead to a megacorp which is fun fun in some sci-fi).

What should it be in an ideal situation? How would you think the problems of to whom it belong be resolved, hopefully, while not killing the profit motive to build such a thing in the first place?