Even if you break up Google or Alphabet, the search division would probably remain a single company. It won't solve anything.
So You get Google Search Inc. Adsense Inc. AdWords Inc, Gmail Inc, I imagine.
This would be just restructuring, Googlers are too smart to get hold back by this and they probably already have an emergency plan if it remotely comes as a possibility.
I don't think it would be possible to split off AdWords from Search. Search would either partner with AdWords or roll its own ads and then we'd be back to square one.
When Bell Telephone was split it was cut along geographic lines. That would also not work on a tech company for obvious reasons --- software knows no borders. I don't know of a sensible way to break up tech giants because the efficiencies of scale create a natural winner take all market.
However Bell was broken up in a consent decree that didn't have to do with its monopoly over the networks, not explicitly at least.
Bell was broken up because they owned Western Electric and used it to vertically integrate the telco stack for the entire country.
A hypothetical breakup of Alphabet could mirror the breakup of the Bell system, as Alphabet controls the data collection -> advertisement stack. Spin off Search + AdWords as an independent business, while services targeting data collection services that feed it (Chrome/Chromium, Android, GSuite, Google Home, etc).
Personally I could see a lot of consumer benefits.
So, as part of the deal, you prohibit the companies from engaging in the businesses that you broke up. So search, inc can't expand to ads, and adwords can't expand to internet search.
Search, inc is still going to want ads, presumably, so they'll contract with someone. Setup rules for the contract. Maybe require at least N ad providers with each getting a minimum of Y% of pageviews, and contract terms have to be FRAND.
Strongly restrict personal information passing between the companies.
Or, i guess you could go all Bell on them and divide the US into different territories and have Pacific Google and Southewestern Google and what not. Would be kind of weird to geofence search and ads though.
Google Search is aleady geofenced. Wven if you switch search language, it will still apply filters depending on the geolocation of the request IP. So splitting Google along geographic boundaries wouldn't change much on the technical side of things at all.
It will, no worries. What would prevent Google AdWords Inc providing ads to Google Search Inc? It's like any other company signing up for an ad network.
My point is that if your company sells information rather physical products then breaking it up is pointless.
I don't think that if Google vanished tomorrow, a new crop of superior search engines would suddenly pop out of the ether to replace it.
Is Google somehow suppressing the creation of a good search engine? No, on the contrary it has created the best web search engine we've ever seen. I would personally be sad if you took it away from me, and I suspect that 99% or more of its users would be in the same boat (don't judge the zeitgeist by web forum echo chambers). You break up monopolies when they are harming users, not in order to cause harm to users.
Google's search engine is a unique portal into the WWW in that it heavily controls what parts of the web people get to see. Opinions can be shaped, facts can be suppressed, lifes can be ruined by the decisions that go into search result prioritizing.
With the world being what it is today, Google Search is in an extremely powerful position. We depend a lot on information that we find on the web. And these free form search queries are the best UI we have at the moment to retrieve it.
It is a good thing that Google Search is good and is getting better, but that doesn't take away from the fact that they wield a lot of power that needs to be checked somehow.
One of the reasons for breaking up monopolies is that they make it harder for newcomers to build something better.