Apple’s share price did actually drop on the news of Steve Jobs’ medical leave, despite what I said yesterday. But today that didn’t seem to matter as the world’s biggest technology company announced record profits.

It was Martin Luther King Day yesterday. The NASDAQ wasn’t trading. That record share price of $348.48 was Friday’s close. Mea culpa. When the market re-opened today, Apple shares dropped almost 8% with more than 7 million shares traded in the first 15 minutes.

But then came all the big numbers: record quarterly revenue of $26.74 billion; record net quarterly profits of $6 billion; earnings of $6.43 per share; gross margin was down a little, a mere 38.5% compared to 40.9% a year ago. That was one of the very few negatives. Apple’s cash reserves now stand at a comfy $59.7 billion.

Apple’s main problem in the December quarter? They sold 16.2 million iPhones. That’s 86% year-on-year growth, $10.1 billion in revenue not even counting accessories. And why is that a problem? “We continue to have a sizeable backlog, and believe we could have sold even more iPhones if we had been able to supply them,” Apple CFO Peter Oppenheimer told analysts.

Terrible business. Especially, as Apple boasted today, that 88% of the Fortune 100 companies are now testing or deploying iPhones as corporate devices.

The iPhone’s success more than makes up for the slight decline in iPod sales, and Apple still represents more than 70% of the MP3 player market. The iPhone-without-a-phone, the iPod Touch, is more than half of those sales.

“We’re extremely pleased with our record-breaking results and customer response to our products,” Oppenheimer said.

Geographically, Apple’s biggest growth zones are their Japanese and Asia-Pacific regions — iPhone sales, for example, more than doubled year-on-year. Overall, revenue in these regions is up more than 50%. Apple says that was part of a deliberate strategy.

Said COO Tim Cook today: “Of the BRIC countries — Brazil, Russia, India, China — we, several years ago, identified China as our top priority and we put enormous energy into China, and the results of that have been absolutely staggering. The revenue from Greater China [mainland plus Hong Kong and Taiwan] last quarter was $2.6 billion, which was up 4x from the prior-year quarter.”

The four Apple Stores in China were, on average, those with the highest traffic and highest revenue of the 323 stores worldwide, and the 87 non-US stores on average generate more revenue than their US counterparts.

Apple sold 7.33 million iPads during the quarter, along with their accessories generating $4.61 billion in revenue. “Today,” Oppenheimer boasted, “over 80% of the Fortune 100 are already deploying or piloting iPad.”

But what of Steve Jobs? There was no new information today. Analysts didn’t even ask directly, with just one question about Apple’s long-term product roadmap. “Part of the magic of Apple is that we don’t let anyone know about that magic because we don’t want anyone copying it,” Cook replied.

There was plenty of Jobs-related speculation elsewhere, though, including Slate’s Farhad Manjoo suggesting Jobs will not return. Jobs, he says, has now achieved his vision of computers as a consumer appliance — a process that started in 1984 with the first Macintosh and reaches its logical conclusion in the iPad.

“You may not like this vision,” writes Manjoo. “Tech nerds, especially, have long criticised Apple and Jobs for infantilising users, for removing people’s control over their machines in order to create more streamlined, easier-to-use gadgets. These complaints are often valid. But they’re also moot, because Jobs has won.”

As I filed this story just after 11am AEDT, Apple shares are trading at just over $340, down around 2% from the Friday close but still higher than anything before the beginning of this year.