Apple's objective isn't to become the largest. Apple does not see this as a winner-take-all platform war. Apple's core values are all about it's ability to change things, it's ability to think different, it's ability to move forward without obstacles.
Apple wants to make, and sell, the best and most beautiful devices they can imagine. For that they don't need to "own the market", their platform doesn't even need to "win". Whenever Apple thought that their platform was limiting their ability to innovate they have dumped the platform and build a better one. That's the kind of business Apple is.
Apple doesn't compete with Nokia for the €40 phone market, Nokia does a great job already in that market. Apple is competing in the high-end smart phone market and only in this small market does it want to "win" in any sense.
Apple sometimes finds itself in a situation where there is not competition, that's fine too. Just don't expect Apple to make something cheap for the lower-end of the market. More often then not, someone else will fill that niche soon enough.
Apple only needs two things: (one) An open market of multiple competing platforms with shared open standards and protocols so that devices can work together. (two) Something special to differentiate itself by, often a level of quality and total integration, the realization of a coherent idea.
About the only thing Apple can't accept is a market where someone else controls an essential part of the market, may it be either some piece of hardware, or software, a protocol, or even the structure of the market itself.
To have someone else control the market would mean that someone else controls the speed of change. It would severely limit Apple's ability to innovate. And it's ability to innovate is the heart and soul of Apple.