Apple's (NASDAQ: AAPL) tablet business is struggling. Last quarter, the company sold just 13.3 million iPads, down 9% from the same quarter last year, and down almost 22% from two years ago.

This is not a one-off occurrence: Apple's iPad business has been contracting for several quarters now. Management had previously downplayed the iPad's weakness by citing channel inventory issues, or a lack of a new model. But at this point, it's largely indisputable: Apple's iPad business, once heralded as the future of the company, is dying.

Meanwhile, Android-powered tablets, led by Samsung (NASDAQOTH: SSNLF), have steadily captured a progressively larger share of the tablet market.

Android tablets are taking over
During its recent conference call, Apple's management rightfully noted that the iPad's decline should be viewed in the context of the larger tablet market: In the U.S. and other developed economies, the demand for tablets just isn't as strong as analysts had believed.

Yet that fails to take into account the relative success of Apple's rivals. In the first quarter, for example, Apple's tablet business declined by 16.1% on an annual basis, according to research firm IDC. Samsung's tablet business, meanwhile, grew 32%.

A similar trend occurred in the fourth quarter of last year. While Apple's iPad did experience modest growth (up 13.5%), shipments of Samsung's tablets exceeded it by a factor of more than six (up 85.9%). In both quarters, Apple's growth was well below the broader market's, while Samsung's far exceeded it.

The difference between phones and tablets
I have previously argued that Apple's share of the tablet market would eventually fall into the single digits -- down from over 90% in 2010. Obviously, in light of the latest iPad sales data, I stand by my projection.

Although the products are less similar, the economics of Apple's iPad business align much more closely with the Mac than they do with the iPhone. The Mac's share of the larger PC market has been growing in recent quarters, but has historically remained well below 10%. Apple's iPhone, meanwhile, has about 15% of the global smartphone market, but is far more popular in developed economies, particularly the U.S. and Japan.

Not so coincidentally, these are markets where carriers offer generous subsidies, footing the bill for most (or all) of Apple's iPhone. Even when subsidies are nonexistent, carriers offer something largely similar in no-cost financing. This stands in sharp contrast to the PC and tablet market, where customers generally pay the entire cost themselves.

When they're on the hook for every dollar, they seem more likely select the cheaper product. Samsung makes a variety of high-end tablets that compete with Apple's iPads (are priced similarly) but it also offers many budget devices.

Why Apple shareholders should care
Apple's CEO Tim Cook said that the company wasn't worried about the iPad -- that the tablet market was still in its infancy.

Worrying may be going too far, but investors should definitely care. Apple remains a great stock so long as gross margins remain high and the company returns cash to shareholders, but the iPad's decline reinforces the concentrated nature of Apple's business: Apple is completely dependent on the iPhone.

That's been true for years, but there had been widespread hope that the iPad would eventually form the second leg of Apple's business. Unless something significant changes, that hope appears to have been dashed.