Apple blew the lid off expectations for its latest record quarter that ended Dec. 25, selling 7.33 million iPads during a quarter when analysts on average were expecting iPad sales of 5.5 million units.

Apple also sold 16.24 million iPhones during the holiday quarter, and while a record, that’s just the tip of the iceberg when considering all those iPhone 4s that it will start selling through Verizon Wireless starting in February.

Executives also pointed out that if they had the supply to meet demand, they could have sold even more iPhones in the last quarter. COO Tim Cook said the company is working to fulfill the orders and will do everything possible to get the iPhone into as many hands as possible at Verizon.

Several times throughout the call, executives reiterated that they’re “thrilled” to be supplying Verizon with the iPhone and fulfill a big pent-up demand with existing Verizon customers and customers who will be new to Verizon. The United States was the last market for an exclusive carrier arrangement.

But the big question looming over the company’s earnings conference call on Tuesday was the news that CEO Steve Jobs is taking a medical leave of absence for an undetermined amount of time.

In response to a question from Piper Jaffray analyst Gene Munster about Apple’s long-term business plan – like how far into the future it goes, COO Tim Cook said that’s part of the magic of Apple and not something he’s willing to share with competitors. But he reassured everyone that the team at Apple feels very confident about the future of the company, its ability to grow share in both the Mac line and smartphones and the early prospects for iPad.

In a press release, Jobs said: “We are firing on all cylinders,” which pretty much sums it up. Even Macs, albeit with a small market share, grew faster than the competition in the PC category, a point that seems to validate the idea that once consumers are introduced to Apple products, like through the iPhone, they start looking at other Apple products.

If Apple executives are the least bit worried about competition from others like Android, they’re not letting on. Cook said current tablets in the market with Android are using a version of the OS that even Google has said wasn’t designed for tablets, and those with a 7-inch screen are too small to be worthwhile. As for those introduced at CES, they’re still lacking specifics on pricing and timing, and mostly could be considered “vapor.”

Looking ahead to the next quarter, Apple expects revenue of about $22 billion and diluted earnings per share of about $4.90.