Antitrust tools are mostly blunt instruments for breaking up monopolies. But, in this case, the monopoly is vested in the Algorithm. You can't split up the Algorithm and parcel pieces of it out to Google competitors. It is a singularity. What competitors would want is access to Google's proprietary database, but that would be like giving away the family jewels. Google wouldn't want to do that. Or would it?
In a way, Google does this now. They give access to the second derivative of their data by letting anyone buy keywords and see the demographics that they produce. This is a valuable service and Google invented it. By rights, the stock should be much higher than it is now, but I digress.
As a monopoly, the antitrust people would ordain that search be set up as a public utility which would then be allowed to collect all the data, even from the Apple fan boys. And the data would be made available to anybody, pretty much as it is now, by purchasing keywords in order to gain access to aggregate demographics, which they could use as they please. Of course, the business would continue to be one of placing advertisements as purchased by the advertisers. So you see, it's not the data that other companies need, it's the function to which they are applied. Google provides this function now, better than anybody else can, for prices which are set by the going rate. However, as a public utility, the profit that Google will make for providing these services will be regulated by the government. Fair and square. That should settle the hash for all search wannabes who think they are smarter than Google.
Of course, that won't happen any time soon, so Google has ample time to make zillions for its patient shareholders. But, when it does happen, Google will finally have to come up with other ways to make obscene amounts of money.