These quantities are expected to hit 200 million chips next year, and only TSMC can provide such capacity, with the CEO Morris Chang indicating that they can dedicate up to two entire plants towards a single customer, a move that might startle NVIDIA, Qualcomm and the rest that use TSMC for their chip fabrication.
The rumor is that TSMC might start supplying the bulk of Apple's future quad-core chips built on the new 20nm process as soon as 2013 in time for the next iPhone. For comparison, current mobile chips are done with 28/32 or 40/45nm, and producing so many chips with the new technology and the yield that Apple demands might literally put the other TSMC clients on the backburner. After all, it will take Q1 of next to fully line up supply and demand for the current 28nm process, which sent Qualcomm's shares down during the summer, and we can imagine the resource shortages if Apple moves in with a new production method.
There were reports that Apple offered a billion to the Taiwanese to secure exclusivity, which the CEO turned down as he didn't want to put all of the company's eggs in one basket, but Apple's cash and persuasive clout is hard to resist, so TSMC might have a resource-allocation puzzle on its hands very soon. For more info how TSMC became the chip giant it is now, you can read our dedicated article on the foundry here.