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What would breaking up Facebook look like?Crack it along its social graph(s) or separate the platform (which would become a regulated utility) from the advertising business.
Mergers offer four broad categories of synergies [1]: demand-side, supply-side, political and administrative. Airline mergers are usually about demand-side synergies. Having more market share gives you better data about future trends. It also gives you pricing power. Media/telecom mergers tend to rely on supply-side synergies: prices won't be raised, but content suppliers can be squeezed for distribution. When Lockheed Martin bought Sikorsky it acquired lots of employees in Connecticut [2]; that bought them some bulldogs in the Congress. (Administrative synergies are mostly B.S.; they fall into the "you have an accounting department, we have an accounting department, combined we can have just one" category and were mostly disproven in the post-WWII conglomerate boom.)
Facebook is a super aggregator [3]; it has both demand-side and supply-side monopolistic synergies. Cracking the demand side means users go to sleep with a Facebook account and wake up with a Facebook No. 3 account. (Or to sleep with an Instagram account and wake up with an Instagram account.) This worked for AT&T and could be done today (at significant expense to Facebook's shareholders as it was to Standard Oil's, AT&T's and Microsoft's). Cleaving social graphs is complicated. But we understand graph theory better today than we did in AT&T's days. Bonus: require an open inter-operability standard if these networks want to interconnect.
Cracking the supply side would involve taking related advertisers and hiving them off into a separate advertising company. The Facebook platform left would be a natural monopoly, regulated like a utility, serving dual profit and public roles. (Messenger, Instagram, M, and other relatively-discrete products would similarly be spun off.)
TL; DR The novelty of breaking up a Facebook is superficial and finds precedent in antitrust enforcement history.
[1] https://www.investopedia.com/terms/s/synergy.asp
[2] http://www.courant.com/business/hc-sikorsky-connecticut-2016...
[3] https://stratechery.com/2017/defining-aggregators/