which 2 letter TLDs are not controlled by states?

Well, almost all of them are ultimately controlled by the nations, but there are quite a few that private companies operate because they've paid the nation to gain control.

But then there's .io (and a few others: .ac, and previously .sh, .tm) where they were actually delegated to a British guy and are now controlled by the private company he started. And according to the British government, they have no agreement with the company, and they receive no revenue from the domain registrations.

.eu :troll:

Supposedly none because they're only given to states, but there're a few that have some murky administrative situations.