“Day-to-day adult supervision no longer needed!” tweeted Google CEO Eric Schmidt early this morning Australian time as the company announced that Larry Page would take over in April.

Schmidt was appointed Google’s “designated adult” in 2001. His hard-headed business approach, honed through experience with Sun, on Apple’s board, and as CEO of Novell, counterbalanced the youthful enthusiasm of founders Page and Sergey Brin. The three made Google’s management decisions as a triumvirate, an unusual arrangement to say the least.

It seems to have worked. Google is the world’s … oh forget numbers. You know what Google is. It’s a verb.

Today they announced quarterly revenues of $8.44 billion, up 26% year-on-year. Earnings per share are $7.81, up 27%. Cash reserves sit at $35 billion. That’s less than Apple’s $59.7 billion, but Google has been on a shopping spree after a period of GFC-induced caution, acquiring 25 companies in 2010 covering everything from social networking and social gaming to speech synthesis and online video.

That’s not to say the Page-Brin-Schmidt troika was performed without treading on toes.

Most famously, Schmidt had convinced the founders to do business in China, despite the obvious mismatch between that country’s internet censorship policies and the company’s pro-free-speech culture. That, and Brin’s personal abhorrence of authoritarianism fuelled by his family history as Jewish emigrants from the Soviet Union. Schmidt was apparently over-ruled in last year’s highly-public threat to quit China. But there’s been a backdown. Google now plans to recover that lost market share.

And Google’s share price, while respectable, hasn’t matched Apple’s meteoric rise these last few years. Through the first half of 2010, it fell against the NASDAQ, presumably thanks to uncertainty over China.

So was Schmidt pushed? Did Page and Brin, now 37 years old, decide they no longer needed a chaperone?

“I don’t think he was pushed aside, but he may have been nudged,” Ken Auletta, author of Googled: The End of the World As We Know It, told The New York Times. He suspects Schmidt just wants a change after a decade as CEO, and he does stay on as executive chairman, “focusing externally on deals, partnerships, customers and broader business relationships, government outreach and technology thought leadership”.

I’m inclined to agree. The shift in Schmidt’s role is relatively subtle. Google is selling it as “plans to streamline decision making and create clearer lines of responsibility and accountability at the top of the company”. Page becomes CEO. Word is he was always the strongest voice in the trio. Brin “will devote his energy to strategic projects, in particular working on new products”.

It’s those new products that fuel the truly interesting speculation. While search advertising remains the cash cow, Google’s ever-multiplying tentacles now reach into cloud computing with Gmail and Google Docs, mobile operating systems with Android, broadband internet services — even a self-driving car.

Indeed, the entire industry is morphing into three competing vertically-integrated stacks. Apple’s iPhone and iPad devices running iOs connecting to services sold through the iTunes Store and App Store. Microsoft’s Windows Phone 7 running on third-party hardware connecting to their Azure and Live cloud platforms, including Xbox Live. And Google’s Android running on third-party hardware connecting to the Googleverse and applications in the Google Market.

That’s a simplification. There are other players, many subtleties. But these big three are drawing the battle lines, and the choices are as much tribal as technological.

Speaking of Microsoft, their turn comes next week. Their quarterly earnings announcement is scheduled for January 27 US time. Sales of Windows Phone 7 reportedly didn’t meet expectations.

Google shares closed at $626.77, down a smidgeon, but recovering and even rising on after-hours trading. And a bonus link: Google’s stock under Eric Schmidt. It just blipped in and it’s a great history!