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The worldwide market for combined shipments of PCs, tablets and mobile phones is expected to total 2.4 billion units in 2013, rising to nearly 3 billion units by 2017. It is probably no surprise that phone shipments will dominate and that PC shipments will diminish. The question is whether Microsoft Corp. (NASDAQ: MSFT) should be worried.

The shipment data comes from the latest research at Gartner Inc. (NYSE: IT) and breaks the device world into four categories: PCs, which includes desktops and laptops; ultramobiles, which includes devices like the Surface from Microsoft and various lightweight ultrabooks; tablets; and mobile phones. Why Gartner has created the ultramobile category is anyone’s guess, but these devices probably should be included with PCs because most, if not all, use the some version of the Windows operating system. The MacBook Air from Apple Inc. (NASDAQ: AAPL) is one exception, and the Chromebook from Google Inc. (NASDAQ: GOOG) is another.

By 2017, Gartner predicts that tablet shipments will total nearly 468 million, compared with a combined total of 368 million PCs and ultramobiles. In 2012, total PC and ultramobile shipments came to 351 million, versus just 116 million tablets. By 2017, tablet shipments are forecast to grow by a factor of four, while PC and ultramobile shipments rise by a slim 4.8%. According to a Gartner executive:

While there will be some individuals who retain both a personal PC and a tablet, especially those who use either or both for work and play, most will be satisfied with the experience they get from a tablet as their main computing device. As consumers shift their time away from their PC to tablets and smartphones, they will no longer see their PC as a device that they need to replace on a regular basis.

And it gets worse for Microsoft and the PC makers:

Growth in the tablet segment will not be limited to mature markets alone. Users in emerging markets who are looking for a companion to their mobile phone will increasingly choose a tablet as their first computing device and not a PC.

The Android operating system from Google dominates the platform market. By 2017, about half of the nearly 3 billion devices shipped will use Android, while Windows and Apple’s iOS/MacOS will take about 15% each. BlackBerry (NASDAQ: BBRY) devices barely make the chart, taking just 0.8% of the market in 2017.

Should Microsoft be worried? The company would be foolish not to be. Its bread-and-butter PC market is shrinking and it has virtually no presence in the huge growth markets for tablets and phones. At best the company can aspire to a distant third place in the mobile platform market while it watches its PC shipments steadily decline. Microsoft’s situation is not desperate yet, but a shrinking market for PCs and Windows portends slow to no growth — and possibly worse.

Shares of Microsoft are down 0.5% at $28.44 in premarket trading this morning, in a 52-week range of $26.26 to $32.89. Except for a dive below $20 a share at the market’s low point in 2009, Microsoft’s shares have traded in a range between about $24 and $32 for the past five years. Nothing in its future would indicate that the top of that range is going to go much higher.