A Time Warner Cable store in New York. (Michael Nagle/Bloomberg)

Time Warner Cable has a plan to kill the set-top box -- that clunky piece of equipment that many cable companies force you to rent for hundreds of dollars a year.

The company has been testing a version of a streaming video app in New York City this week, and although it's a limited trial run, TWC chief executive Rob Marcus has much wider ambitions for the service.

"Where we're headed," Marcus said on an investor call Thursday, "is the ability of customers to access the complete video product without having to rent a set-top box from us, whether they use a Roku or another [Internet Protocol]-enabled device."

Ultimately, TWC customers will be able to get all the same channels through the app that they currently get through their physical set-top box. While some companies may envision keeping the box around while also offering a streaming app, TWC believes it could save a lot of money by not having to pay for and rent out boxes at all (not to mention the time-consuming installation service that comes with it).

Through the app, customers will eventually be able to buy not just their traditional cable line-up but also modified bundles targeted at the cord-cutters among us, Marcus said. He also ruled out the company's participation in a major upcoming airwaves auction, putting to rest (at least for one company) rumors that cable firms may soon move en masse into providing cellular service.