Apart from all the political discussions, I have no idea how the buyer is supposed to buy out just some regional markets.

Would development still be done by the original company, and the new owner just operates regional data centers? But without inter-connectivity? Without being able to influence development, or offer access to the developers for debugging and ops? Seems exceedingly unlikely.

Otherwise, do they get a code dump of a huge, complex code base, and are supposed to continue development on their own? With the original TikTok still operating in other parts of the world, and slowly diverging? I can't see that happening either.

Would they buy the brand name too, and the rest of the world would start using a different name?

That all seems pointless. The only thing that makes sense to me is taking over globally.