When Eric Schmidt handed the reins of CEO at Google back over to cofounder Larry Page recently to take on the role of the company’s executive chairman, with a more external focus, news reports predictably recounted his oft-made joke that his role at Google had been to provide “adult supervision” for the company’s cofounders, Page and Sergey Brin. Indeed, no one could argue that in Schmidt’s ten years at the helm, Google had grown up into an extraordinary force in global business. Schmidt’s track record atop the leader in Internet searches stands as remarkable story of steady growth, expanded reach and influence, and an innovative management style that will remain scrutinized as Schmidt, 56, takes on new duties.

Google now produces close to $30 billion in annual revenues, and its domain is growing well beyond search. The company’s YouTube unit, with some 40 percent of the market for Web videos, is generating profits for the first time, and its Android operating system hums at the center of more smartphones than Apple’s iPhone.