Akamai manages and delivers Internet content for clients like News Corp. (NWSA), Facebook (FB), Apple (AAPL), Nintendo (NTDOY), and Netflix (NFLX). The more content is demanded, the better Akamai does. As broadband speeds increase, more people watch video online, play games, and download software. The company said during its conference call with analysts that all of those businesses added to its bottom line.

Akamai’s net profit, excluding one-time items, jumped to 51 cents per share, up from 36 cents in the first quarter of 2012. Revenues rose by 15%, to $368 million. Analysts had expected profits of 47 cents per share and revenues of $358.1 million. Margins improved greatly, with costs growing by just 8%. Meanwhile, the company forecast a healthy second quarter as well. As of midday Thursday, the company’s stock had soared by more than 20%, to $43.45.

The results were good enough to more than offset the “winding down” of some media accounts — in particular a large video provider that is widely believed to be Netflix. That company is building out its own network and transferring more of its traffic management to it and away from Akamai and other providers. For Akamai, the wind-down is expected to be complete by the end of next quarter.

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When Netflix last June announced the creation of its own network, called Open Connect, Akamai’s stock took a hit. But investors realized soon enough that even though Netflix was a huge customer, the move would actually be good for Akamai in the long run. Margins from Netflix are tiny because of the video giant’s negotiating power. As the wind-down continues, Akamai will have more bandwidth available to sell to smaller customers at higher prices. Netflix is a special case: Few companies, even big ones, want to manage their own traffic on their own networks. It makes economic sense for Netflix but (at least for the foreseeable future) not for companies that are in businesses other than just delivering content to end users. Google’s YouTube (GOOG) is another company that manages its own content delivery network.

Besides the jump in average broadband speeds, the “State of the Internet” report noted the recent jump in cyberattacks, as well as the increasing sophistication of such attacks. The company benefits from this, too. Akamai reported that revenue from its “performance and security solutions” was up by 17% over the year-earlier period, to $157 million.

During the conference call, CEO F. Thomson Leighton said:

“It has become abundantly clear over the past several months that any company doing business online needs to be diligent about security. Online attacks are becoming larger in size, more frequent, more varied and sophisticated, and they are being launched on a global scale. For example, the attacks we witnessed while defending our U.S. banking customers during Operation Ababil came from servers located in more than 100 countries. These highly distributed attacks demonstrate why companies need to think about web security differently and also why we believe that they need the distinct advantage provided by our distributed platform.”