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Steve Jobs announced on Monday that he is taking another leave of absence from the company — of unspecified length — to deal with his health. Although he will remain CEO, Apple’s (s aapl) chief operating officer Tim Cook will be running things in Jobs’ absence. While the company is on firm financial footing, and is expected to beat most analysts’ estimates with its quarterly earnings tomorrow, the news is almost certain to rattle investors, and could put continued pressure on the stock as the markets try to figure out what Apple might be like without its charismatic leader.

The company appears to have deliberately chosen to release the news on Martin Luther King Day, in order to give investors some time to think about it, since U.S. stock markets are closed. But Apple shares dropped dramatically on foreign markets, falling as much as 7 percent in Germany at one point after the news was first reported. Apple likely also chose to make its release just before it comes out with its financial results, since that should focus investors’ minds on the performance of products like the iPad and the iPhone 4 instead of on the CEO’s health. Most analysts have said they are expecting another blockbuster quarter from the company.

Despite what is expected to be good news on the financial front, the Jobs announcement is almost certain to re-ignite criticism that Apple has not been as forthcoming as it should be about his medical status. Jobs was widely expected to appear at a recent press conference announcing Verizon’s (s vz) launch of the iPhone, but Tim Cook appeared instead. Others noticed that during the Apple developers conference in September, Jobs handed off a lot of the presentation to Cook and others — although he has been doing that more over the past year, in what is likely an attempt to shift the spotlight away from himself and show that Apple has other executives who can carry the torch if necessary. (The company continues to argue with shareholders over its succession planning.)

Apple came under fire in 2008 over repeated reports that Jobs was more seriously ill than the company had acknowledged — based in part on his gaunt appearance at several events — but there was no official news until Apple announced in January of 2009 that he was taking a medical leave. Shortly thereafter, Jobs was required to have a liver transplant. Some argued that his personal health was no one’s business, but SEC rules require companies to inform shareholders and the public markets about material facts, and Jobs having complications as a result of potentially fatal illness was seen by many as a material fact. One of Apple’s own directors later said that the company should have gone public with the news, and that he regretted not resigning over Apple’s decision to keep quiet.

The focus on Jobs and his health stems from the fact that Apple is one of the few major corporations whose fortunes are tied so closely to its founder and CEO. Most other companies with a $300-billion market value and revenues in the $25-billion range may have prominent chief executives, but few of them are seen as having so much control over the products their companies produce — and even fewer are as charismatic and widely admired as Jobs. Some have estimated that the stock trades between 10 and 25 percent higher than it otherwise would, based solely on Jobs being the CEO. During the latter part of 2008, after rumors of Jobs’ health began to accelerate, the stock lost more than 50 percent of its value, although several analysts have told Reuters (s tri) that they don’t believe the latest absence will affect the stock that much.

On the weekend, a Smart Money columnist wrote a piece entitled “Are Apple’s Best Years Over?” In it, James Stewart argued that while the company has been hugely successful with the iPad and the iPhone and its MacBook laptops, “I’m not sure what worlds there are left for Apple to conquer,” and said the stock could come under pressure because it has climbed more than 80 percent in the past year, and is up by over 400 percent from its low in 2009. Rightly or wrongly, the news of Jobs departure is going to cause many investors to echo Stewart’s question.

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