It's the US church, with branch offices scattered around the world. That's not what we want, but it's what has developed over the years, and we need to change it. While UB churches in other countries have willingly followed the Constitution of 1841, it has no true authority over them. A document written by United States people has no actual authority over people in Jamaica, or Hong Kong. People in one country cannot tell people in another sovereign country what to do.
Sovereignty exists at a lot of levels.
The US can't tell Turkey how to run its court system. GM can't tell Ford where to build a factory. UCLA can't tell Indiana how to hire a basketball coach. But the way we've been set up, the USA pretty much runs the show and sets the rules. And that needs to change.