How long can Apple’s growth in enterprise stay this quiet?

Apple chief operating officer Tim Cook said he envisions an entire business run from a single iPad.

He’s probably not that far off. Apple’s iPad made a serious push into the enterprise space in the fourth quarter last year, and 80 of the largest companies in the world on the Fortune 100 list are now testing or deploying iPads. That’s up from 65 of the companies on the Fortune 100 list the last time Apple reported its quarterly earnings in September.

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The iPhone also increased its presence in the enterprise space, with 88 of the companies on the Fortune 100 list either testing or deploying applications on it. The iPhone was deployed with 85 of the companies on the Fortune 100 list at the end of its last quarter in September.

Among the latest companies to join the list of those deploying the iPad and iPhone are some financial services companies like JP Morgan Chase and Wells Fargo. Which is saying something — typically the enterprise is a very slow-moving space, and financial services are reluctant to pick up new technology for fear of it failing at inopportune times.

iPad sales were also a whopping 7.3 million for the fourth quarter last year, up from 4.19 million iPads sold during the third quarter. Apple sold close to 16 million iPads in 2010, despite the fact that it only began shipping the devices in April. Cook made the comments on Apple’s quarterly conference call to discuss earnings.

Apple hasn’t been particularly silent in its enterprise strategy — going so far as to snap up former Research in Motion talent to help turn its devices running on the iPhone operating system into viable enterprise tools.

Apple’s App Store recently crossed the 300,000-app milestone and sports a number of popular business applications like Yammer and Chatter. The most popular category for apps on the App Store was also the business application section, where downloads grew by 186 percent in 2010 compared to 2009, according to a recent report from Distimo. A large number of organizations — especially those on the Fortune 100 list — are now developing custom applications for their businesses as well, said Apple chief financial officer Peter Oppenheimer.

“You could run your whole business off an iPad or an iPhone,” said Apple’s Cook. “The list of things you can do on those devices today were simply unimaginable a few months ago. And we have a higher customer satisfaction rating in the surveys for enterprise — everyone just wants to use an iPhone and the companies are letting them.”

Research in Motion is still the reigning champion of the enterprise space for mobile phones. The iPhone 4 accounted for more than 30 percent of mobile device activations for enterprise purposes, and more than 10 percent of activations were iPads. But those numbers are dwarfed by Research in Motion’s 55 million BlackBerry users — a massive share of which are enterprise users.

Cook was quick to point out that Apple would add a chunk of new enterprise features in each new iteration of the iPhone operating system. But because Apple’s products are traditionally consumer-facing devices, the newest enterprise updates tend to get lost in the noise and excitement about other features.

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The iPhone 4 and iPad are still facing some pretty ravenous demand, Cook said. Apple is getting closer to an equilibrium point where the amount of iPads and iPhones it was producing is equivalent to the demand. But the company still isn’t doing enough to make more iPads, he said. An analyst with Wall Street firm Piper Jaffray said Apple could probably sell 21 million iPads next year as a result of its presence in the enterprise space. Maynard Um of UBS Investment Research said in November that Apple could sell up to 28 million iPads in 2011, as well.

Said Cook: “I feel great that the demand is so high, but at this point I’m not going to predict where supply and demand will meet. The results have been absolutely staggering.”