ARM (ARMH) shares have shot up this week on the speculation, bringing them to levels they haven’t seen since 2002. As of now, it looks like it would cost a suitor more than $8 billion to bag the company.

So what gives? Does Steve Jobs really want to fork over billions of dollars for this company?

The answer, I believe, is yes – he very well might. But there are dozens of other tech companies, and probably a few regulators, who wouldn’t want to see that happen. Why? Read on.

First, try to get past the fact that you’ve never heard of ARM; it is arguably the most important player in the mobile hardware business today. (Take a look at this feature I wrote about the company last year.) The mid-sized U.K. firm develops the basic chip designs at the heart of practically all of the world’s cell phones, from the no-frills handsets common in rural India to the latest iPhone. ARM’s specialty is designing elegant, battery-sipping silicon that’s small enough to fit into gadgets and powerful enough to make them hum.

ARM doesn’t get much attention because of its unique business model. Rather than build its own chips, it simply licenses blueprints to companies including Qualcomm (QCOM), Texas Instruments (TXN), Nvidia (NVDA) and Apple (AAPL). Those companies then customize the designs and give ARM a small cut of every sale. The more sophisticated the phone, the more ARM technology it needs, and the bigger the payment ARM gets.

That’s a very different model from Intel (INTC), the biggest and best-known chip company in the world. Intel designs and builds its own chips in a soup-to-nuts approach that yields big revenues and healthy profit margins. The advantage to this model is that Intel has the talent and resources to produce some of the most powerful chips in the world, using the most sophisticated manufacturing methods. The disadvantage is that Intel makes a limited variety of chips, and there aren’t a lot of options for customization. Customers pretty much have to design their products around what Intel’s selling, not the other way around.

Lately Apple has shown a keen desire to exercise even more control over how its products work; the ARM-based A4 chip in the iPad was designed specifically for that device, and similar Apple-only chips are sure to appear in future iPhone and iPod designs. In fact, Apple gets roughly two thirds of its revenue from products that run on ARM-based silicon today, and that proportion is likely to increase as the iPhone, iPad and iPod touch grow in popularity.

Given its high reliance on ARM technology, Jobs might figure it makes sense to just own the company outright. He certainly can’t allow ARM to get swallowed by a competitor.

All of that said, there are several reasons why Apple might not actually end up owning ARM.

For one thing, there are too many other influential companies – folks like Google (GOOG), LG, Marvell (MRVL), Nokia (NOK) and Samsung – who depend on ARM’s technology to run their businesses, and they are sure to start a bidding war if they believe ARM is in play. Those companies might not have as much cash as Apple, but they can raise a stink.

And then there are the regulators. With so many companies threatened by the prospect of Apple buying ARM, some regulator somewhere would certainly argue that a sale would be bad for competition in the global mobile market. If they allowed Apple to buy ARM at all, I imagine they would demand assurances that ARM technology would continue to be available to Apple’s competitors under decent licensing terms.

Bottom line: It’s easy to see why Apple might want ARM, harder to imagine a deal going through. Can you imagine Steve Jobs owning the intellectual property behind the world’s cell phone chips, and happily licensing it to competitors who are building phones with Google and Microsoft (MSFT)? Me either.