Will anybody ever "own" all the market slices Google currently plays in? I _very_ much doubt it.
Will the Google Search engine remain an effective monopoly? I doubt that too - I remember when Alta Vista was world-changingly amazing! I suspect Google have deeply entrenched themselves in the employment market for people being very smart about making search better, and the bar is way higher so I doubt it's ever going to be a couple of compsci/linguistics phd students who topple the industry (the way Alta Vista fell), but things like DuckDuckGo and Blekko exist - and no doubt other more academic and less well know ones too, it not impossible (in my opinion) that someone will roll out a "instantly and obviously better than Google" search engine one day.