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.
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.