Google is able to use its lead in search to exert undue influence on other markets. Google can (and has) ocassionaly placed banners suggesting a switch to chrome, influencing the browser market. Google showcases YouTube videos above other video results, regardless of the relative merits of the videos. Similar things in other verticals.
Additionally, search dominance leads to dominance in the related search ads and text ads generally space. In part, because of market size, Yahoo was unable to attract the same kind of advertising market as Google, and famously chose to contract that out to Microsoft, which also was unable to make it work well. I was at Yahoo during parts of that time, and my feeling is that market size wasn't a big part of that failure, but it could be argued that it was a part.
Is any of this compelling enough to be worth an anti-trust case? I don't think so, but maybe?
How could you break up Google if this was considered egrigious enough? Split into several actually separate companies: software, containing chrome, android, and chrome os; search, providing web search apis, but not a front end; advertising, providing advertising apis, but not hosting any sites that use then; consumer services, including a web search front end, Gmail, YouTube, etc; business services, including the Google cloud stuff and maybe g suite; I dunno about the alphabet soup bits. Make the search and ads services contracts be on FRAND and public terms.
