> Just use the size of the parent company, you say? Okay, which is the parent company, Google or Vanguard?

Could you maybe tie it back to majority control? Alphabet is one company because it actually has a controlling stake over Google, YouTube, Android, etc. Whereas Vanguard is just a minority shareholder in Google.

> And even if you could do it, you would then create a perverse incentive for the government, because then breaking up those large companies into smaller ones would reduce tax revenue. When you should just break them up to begin with and actually solve the problem.

The idea is that you wouldn't need to government to actively break up companies, they'd do it themselves (or get outcompeted). I will admit that this is very much unproven theory though (but I'd certainly be interested in people investigating the theory more formally if nothing else).