For a point of reference here have a look at how many independent companies share the “Sparkasse” or “Raiffeisen” trademarks and Logos on Europe.

We can compromise and say "none" :P

There will probably be trademark usage agreements, like with companies who split themselves like Motorola Solutions and Motorola Mobility (owned by Lenovo) both license the Motorola trademark from Motorola Trademark Holdings, LLC unclear who owns the holding company.

Trivialities that antitrust regulations already cover. It would not be the first time a company has been broken up.

You didn't answer the question.

I don't have to: I'm not a judge specialized in antitrust law and I don't have access to Apple's books to determine what would be more appropriate.

But a judge can, and will (if asked to), because - as I said - it's hardly an unprecedented situation. Just to mention one, AT&T still exists as a brand but was once broken up.