If argue it's when one has "more leverage than any single other party", either on the buying or selling side. And it could be based on a raw percentage of units or market revenue, whichever portion is bigger.
Say one buyer/seller with 51+% of a market by unit or revenue would be subject to anti-trust scrutiny. Perhaps another tier requiring more drastic measures, such as breaking them up.
Leverage isn't about "the market", either. It's about the individual people, and their situations. The iOS App Store doesn't give Apple much leverage over iPhone users, but iCloud does – and, to a lesser extent, iMessage¹ and FaceTime do. (The flipside of the iPhone's many planned obsolescence strategies is that you have to choose whether to remain within Apple's ecosystem every three-to-five years, and iPhones are expensive.)
The iOS App Store does give Apple significant power over the authors of apps. Even if the App Store doesn't provide a chokepoint by itself, the iPhone “ecosystem” as a whole does. It's a different thing to antitrust, though the more egregious offenders might also constitute monopolies for antitrust purposes.
On Cory Doctorow's "competitive compatibility" / "adversarial interoperability" theme, a company called Sunbird Messaging claims to have made an iMessage clone for Android. It's proprietary, and might turn out to be vapourware, but I'm hopeful.
This returns us to the problem of defining the market, however. Platforms, specifically, exploit this ambiguity by escaping straightforward definitions of market share.
Say one buyer/seller with 51+% of a market by unit or revenue would be subject to anti-trust scrutiny. Perhaps another tier requiring more drastic measures, such as breaking them up.