OTTAWA — Research in Motion, maker of the BlackBerry, is weighing the possibility of selling all or part of the company. But does it make sense to break RIM in two?

A report in The Sunday Times indicated that Research in Motion could split the handset division into a separate company or sell a large stake in company. While people close to RIM dismissed the idea as a “silly fantasy” in a Globe and Mail article, shares of the company tumbled on Monday.

Either option faces considerable hurdles, starting with Thurston Heins, the chief executive. He has repeatedly said the company’s best hope lies in rekindling Americans’ love for the BlackBerry through phones based on the new touchscreen-based operating system that will come to market later this year.

“RIM has hired advisers to help the company examine ways to leverage the BlackBerry platform through partnerships, licensing opportunities and strategic business model alternatives,” Tenille Kennedy, a RIM spokeswoman, said on Monday. “As Thorsten said on the company’s fourth-quarter earnings call: ‘We believe the best way to drive value for our stakeholders is to execute on our plan to turn the company around.’ This remains true.”

As in the past, Facebook and Amazon were cited as likely buyers of the handset business, which accounts for about 80 percent of RIM’s revenue. With its own line of phones and, more important, its own mobile operating system, Facebook could go up against Google, which uses its Android mobile operating system to promote its other businesses. Some analysts speculate that Amazon wants to add smartphones as a complement to its Kindle tablet business.

While those are plausible motives, buying RIM may not be the ideal way into the handset business. RIM’s current BlackBerry business is based entirely on a line of phones that have fallen out of favor with American shoppers. BlackBerry’s current growth comes from developing markets where wireless network limitations mean the phones outperform Android-based phones and Apple iPhones. But those sales generate lower profit margins for RIM than sales in the developed world, and network upgrades now under way will soon erase the company’s advantage.

Given that, neither Amazon nor Facebook would probably have much interest in RIM’s legacy handset business. They would instead be buying BlackBerry 10.

But BlackBerry 10 is well behind schedule and still without a specific release date, although prototype phones using a still unfinished operating system have been made available to software developers. RIM claims that a sweeping round of layoffs now under way, which may number in the thousands, will leave BlackBerry 10 untouched. Even so, it is difficult to imagine that the situation will help it retain and attract the talent it needs to bring the new phones to market.

In any case, both Facebook and Amazon already have larger technical resources than RIM and seemingly unlimited access to capital. With those resources, they could develop their own phones without buying the uncertainty of BlackBerry 10 or the headaches of RIM’s legacy business.

Amazon and Facebook, along with Microsoft, also pop up as potential buyers of RIM’s much smaller services business.

The service business is essentially the unique global network. The network allows RIM to provide unusually high levels of security for corporate and government users, who install special servers in their computer systems and who pay license and technical support fees.

There are indications that increasing numbers of cost conscious corporations have concluded that not every employee needs the same level of wireless e-mail security as, say, an F.B.I. agent. So what is already a small part of RIM’s business may become even smaller.

Nor is it clear that the infrastructure behind the network is all that desirable. The highly centralized system dates back to the late 1990s. It is showing its age with failures like the one last October that shut down BlackBerrys throughout much of the world.

RIM’s network, however, has one significant feature that probably cannot be duplicated. The company has direct connections into the networks of 650 wireless carriers and wireless service resellers worldwide. Those connections are a crucial factor behind the BlackBerry’s vaunted security.

Because the BlackBerry was the first, and for some time the only, phone that allowed carriers data services, they were willing to give it special access. But some analysts have reported that the rapid decline of the BlackBerry in the United States is causing some American carriers to rethink that relationship.

The arrangements between RIM and the carriers are confidential. But there is speculation that the connections would not automatically transfer to a new owner. It is not clear why a carrier like Verizon would give special access to Facebook rather than Google or Microsoft over Apple.

As RIM and its outside advisers consider a breakup of the company, they will no doubt recall the fate of Palm, the company that effectively created and defined hand-held computing.

In 2003, when BlackBerrys and other smartphones were eating into the hand-held computer business, Palm spun off its software business as PalmSource in the hope that other hardware companies would adopt its operating system.

But neither that nor subsequent events, notably the acquisition of Palm by Hewlett-Packard in 2010, sparked a turnaround. Both the Palm name and its last products have vanished from the market.