Ever since Time Warner (NYSE:TWX) dropped the "AOL" from its name two years ago, the symbolism has been crystal clear: The company considers America Online the albatross around its neck. The notion that the company might spin off its struggling online unit has been making the rounds for some time, and Time Warner's CEO formally brought it up during May's annual shareholder meeting.

However, ditching its online business would be a colossal mistake. Whether AOL is redistributed as a shareholder spinoff or taken public as an exit strategy, it won't solve Time Warner's stagnant share price. In fact, it could make things worse.

Too much has been made of America Online's fading subscriber base. Yes, its membership peaked in September of 2002, when 26.7 million users kicked off their web-enabled experiences with "Welcome!" and "You've Got Mail!" Every passing quarter has been soured with defections, and AOL now stands at just 20.8 million subscribers.

The media tends to play up AOL's image as a dinosaur, a dial-up connection on training wheels in an age of freewheeling broadband excitement. I won't argue with that -- but if that's all you know about AOL, you're missing the big picture.

America Online has been in the process of repositioning its AOL.com site -- once just a place for AOL users to check their mail, or for outsiders to download AOL's popular Instant Messenger software -- as a full-blown portal. If AOL succeeds, it will not only reach back into hearts and wallets of former users, but also draw in folks with no prior connection to its service.

AOL has also been busy with promising broadband-friendly ventures like a comparison travel-shopping site and a partnership with XM Satellite Radio (NASDAQ:XMSR) for streaming audio content. Its prospects are bright.

True, its flagship America Online service isn't the same hotbed of activity that it was a few years ago, but it's still very relevant. Does anyone want to argue that an audience of more than 20 million users, all willing to pay a premium for a more handheld online experience, isn't a marketer's dream audience?

Tomorrow came a day early
The argument that Time Warner would be nuts to shed AOL isn't grounded solely on future dynamics. America Online is important to Time Warner right now. Crack open last week's quarterly report to see exactly I mean.

Time Warner's June quarter was a dud. Operating margins contracted slightly on a small dip in revenue. It wasn't pretty. However, AOL stood out as the one pretty face in a very ugly class picture. America Online's subscriber revenue dipped by 9%, naturally, but advertising's top line soared by 45%. As anyone who has been impressed after eyeballing a Google (NASDAQ:GOOG) or Yahoo! (NASDAQ:YHOO) income statement can tell you, that's where the fat margins go to party.

Through the first six months of 2005, AOL's revenue has fallen from $4.4 billion to $4.2 billion. However, thanks to the robust world of web-based advertising, operating profits have gone from $553 million to $692 million in that time. In other words, over the past year alone, operating margins have shot up from 12.6% to 16.5%.

Even more encouraging: When you compare the March and June quarters of 2005, you'll see that while revenues had a sequential dip, operating income increased.

Let the media stir up the hullabaloo stew by pointing to subscriber defections or noting that the parent company's still smarting over the old AOL's aggressively improper accounting practices. Yes, it's all true, but it shouldn't take anything away from AOL's bottom-line production right now. AOL may be the wild child of the Time Warner family, but it had sharpest spike in operating profits in an otherwise moribund family portrait.

Before you say "Goodbye!" to AOL
Time Warner's debt has dropped to a manageable $13 billion, so it's not as if ditching AOL is a top priority. Sure, the timing may be right to put an online giant into play, especially with companies like InterActiveCorp (NASDAQ:IACI) and CNET (NASDAQ:CNET) are gobbling up smaller players. Even with the defections, AOL is worth more today than it was when its moniker was erased from Time Warner's name and ticker symbol in 2003.

But isn't that the very reason why Time Warner should appreciate what it has? AOL's operating profits have improved by 25% so far this year, and there's no reason why that can't keep going as online advertising becomes a thicker slice of the pie. Why ditch it when the free cash flow is trickling in? Why unload a property to someone who will simply flip it for more later, like Warner Music Group (NYSE:WMG) after its public debut?

Still not convinced, Time Warner? That's fine. Go ahead. Dump AOL. I'll be the one there with open arms and an open portfolio, waiting to reap the tasty fruit you were too lazy to harvest.

In the 1990s, David Gardner bought America Online for the real-money Rule Breakers portfolio and saw it soar by 2,418%. Want to see what the Motley Fool Rule Breakers newsletter service is nibbling on these days? Check out a free 30-day trial subscription.

Longtime Fool contributor Rick Munarriz has been an AOL subscriber for more than a dozen years. Yes, he's the one. He does not own shares in any of the companies mentioned in this story. The Fool has a disclosure policy. He is also part of the Rule Breakers newsletter research team, seeking out tomorrow's ultimate growth stocks a day early.