The company that makes the search engine and the company that sells the ads to the advertiser can be different companies, in the same way that you can put Ad Words on your website and they'll show ads based on the content of the site even though you aren't Google.
So assuming the company is splits into Google and AdWords,
would Google be forced to work with AdWords or are they allowed to use different providers? Are they allowed to create their own competitor to AdWords? Which problem is this solving?
Yes, they'd be allowed to use other ad providers, and hopefully it would be illegal to penalize them for constantly running some multi-armed-bandit trials across multiple ad providers.
Then AdWords would draw the short end of the stick because their product would become commoditized. Google would still hold the same market power as before. Ad quality might go down because there are multiple providers. Overall I don't see the upside.
Maybe something that would make more sense is if Google was split into two or more search engines, each of them would get a copy of the current source code and data.
