[NoMoreNicksLeft]

No, they would certainly not be free to do business with whomever they want. There's a reason the Baby Bells didn't all just enter into a partnership with each other the day after the breakup... they were not permitted to do so.

If/when business was unavoidable between two offspring companies, at minimum, I would expect them to have to inform the FTC, justify how it was unavoidable, and make the details of the transaction public. If someone complained that it wasn't unavoidable, quite possibly there would be additional penalties leveled on each of the participants.

It's not like some Monty Python character waves a wand and declares "you're not n different companies", only to wander off and never exercise oversight. Mind you, I don't think there's enough political capital in the world to manage to break Google up, but if it did happen then the judgement will have the teeth to make sure they're actually broken.