To name only two: AdWords / AdSense is the "auction model" that made Google famous as an online ad brand and is the one they developed (mostly) in-house: advertisers bid on ad impressions, publishers get paid for offering slots on their pages to do the impressions. It's a very hands-off model in that advertisers don't need to control what sites their ads run on and site owners don't need to control what ads get run; Google handles all that handshaking (and brokers all that money).
That model doesn't work at all for a lot of companies that need way more control over the content shown on their pages (either because they have serious concerns about brand-image that they're unwilling to hand to a third party or they're just wedded to the traditional "steak dinner and fancy suits" advertising model and aren't comfortable working with their advertisers at arm's length). So Google also sells a suite of data-management products for companies that broker their advertising clients directly but are vending ad space on digital services. This is the DoubleClick model: it's (for example) the New York Times's pages and the New York Times's ad clients but Google's infrastructure physically vending the ads, tracking conversion data, tracking completion of advertising contracts, running predictive models to see how valuable ad slots can be, etc.
To the layperson, this is just all "ads," but a not-very-sharp knife can be driven clean through these two business units (from the outside. From the inside, they are no doubt built atop the same Google special-sauce NIH fabric, so it'd in practice be a colossal pain in the ass to divest either of them; either one will have to be rewritten to work as a mundane cloud service or the company carved off will be taking a copy of Google's infrastructure special-sauce with it, running Borg and the logging infrastructure, using stubby and dapper, resolving global resource contention with chubby, etc... All stuff Google really doesn't want to compete with in the holistic way it's woven together inside their house).
I think "colossal pain in the ass" underestimates the order of magnitude of pain it would involve (borne by the hapless engineers, no doubt). Divesting the Cloud part of Google (IE moving Cloud into its own independent "prod2") is also somethinig interesting to think about.
And you really think that the government is going to go that far or that it’s a good idea?
But they would farm that ad space to multiple exchanges that would be competing for both advertisers and space, and so profits from running the ad exchanges would go down and those ad exchange profits would not be flowing to Google.
I'm neither arguing for nor against this, but that's conceptually how it would work.
But in any case if it's anything like the breakup of Ma Bell, stockholders would wind up with separate shares of both 1) the products and 2) the ads. Which one calls itself "Google" is just branding. (Although obviously the search engine would keep the brand.)
Win???
Of course, that's against not just more tracking/sharing as you mention, but also probably significantly worse ad loading times and bloat in general.
It's awfully hard and hypothetical to estimate the impact of either.