(Update: tr.im will live to see another day as Nambu has decided to keep the URL shortening service alive after announcing earlier this week it was closing down. TechCrunch points out this the decision could still let Nambu sell the business.)

The URL-shortening market is a fascinating business, partly because a viable business model has yet to evolve despite their growing popularity.

For example, everyone loves bit.ly (especially after Twitter decided to make it the default URL shortener) but bit.ly is still trying to figure out how to make money – a news service is currently front and centre.

Given the absence of a business model and the lack of revenue, it should come as no surprise that a popular player has bit the dust. Nambu has decided to shut down tr.im after failing to find someone to take it over. (Update: bit.ly has offered to host tr.im’s URLs, according to Mashable.)

While it’s always unfortunate to see interesting start-ups disappear, the reality is no one is willing to pay for a URL shortening service.

If you’re bit.ly and lucky enough to find venture capital, you have the luxury of time to see if a business model can be created. If there’s no sugar daddy paying your bills, then it’s a business activity that can suck up time, resources and money.

Given this reality, it’s impressive that tinyurl.com (the Google of the URL shortening business) has been around for such a long time.

Of course, it helps that founder Kevin Gilbertson is a one-man operation content with make a living, while riding a unicycle in his spare time.

Maybe that’s the secret to a successful URL shortening business – you keep costs extremely low and generate enough revenue to operate a skeleton staff.

Here’s a snapshot of the leading URL shortening services, according to Compete.com. Of course, this only takes into account people within the U.S. who visit these Web sites.