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What made them big in the first place were the iPod/iTunes/iPhone and the ludicrous revenues from the App Store.The iPod/iPhone yes, but "in the first place" the App Store was insignificant (the remenues at 2010 was < 2 billion dollars worldwide, so Apple's take was less than $600 million).
For comparison the iPod had that profit already in 2004, and around 3 billion in 2010 (when the iPhone had already started replacing it).
So, the App Store was hardly ludicrous revenue for its first 3-4 years, in fact less than 10% of Apple's revenue. The iTunes store even less so.
It's the iPod and then iPhone that made Apple's dominance. The big store profit came later (and the iTunes/Music profit never was that big).