The obvious place to start splitting is to separate search from other things, like a non-search ad business, an OS, a browser, a mail client, a mapping and navigation business, and hey, another OS.
But I don't think it's impossible to split up search, either. I'm sure that Google doesn't just have 1000s of people working together in one big room with no structure. Their current organizational lines could tell us a lot about useful ways to break it up. Historically, for example, there were search infrastructure providers like Inktomi that sold services to consumer-facing search engines. Maybe a crawling-and-archiving group is separable; there are times I sure would have paid Google to use their crawl rather than doing my own. Parts of search were previously separate companies that perhaps could be spun out again. E.g., a lot of the structured-data stuff was once Metaweb.
But I don't think it's impossible to split up search, either. I'm sure that Google doesn't just have 1000s of people working together in one big room with no structure. Their current organizational lines could tell us a lot about useful ways to break it up. Historically, for example, there were search infrastructure providers like Inktomi that sold services to consumer-facing search engines. Maybe a crawling-and-archiving group is separable; there are times I sure would have paid Google to use their crawl rather than doing my own. Parts of search were previously separate companies that perhaps could be spun out again. E.g., a lot of the structured-data stuff was once Metaweb.