More than half of them — 56% of all households with broadband Internet access — now have at least one TV set connected to the Internet, according to a report from Diffusion Group, “Defining the In-Home CE and Network Ecosystem 2013.” About two-thirds of the nation’s homes have broadband.

While viewers use a variety of means to get Internet video from Netflix and other services onto their TV screens, it appears that smart TVs are increasingly in favor, though most people are still porting video content through game consoles like the Xbox 360 (MSFT), the Sony PS3 (SNE), and the Nintendo Wii (NTDOY). About 62% of households own such a device, which are used about a quarter of the time for TV viewing, on average.

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But smart TVs are coming on strong, growing faster than dedicated Internet-to-TV devices like Roku or Apple TV (AAPL). About 14% of broadband households own a dedicated device, while about 25% own a smart TV. Ownership of smart TVs has doubled over the past year, while ownership of dedicated devices grew by only two percentage points. But only about two-thirds of smart TVs are actually connected to the Internet, according to the report.

Another report, this one from NPD Group, found that by next year, all of these means of connecting the Internet to TVs will eclipse connections via Blu-ray players. For now, more people are connected through Blu-rays than through smart TVs, but that’s swiftly changing — another sign of people moving away from movies on discs. The NPD Group report, “Connected Home,” also found that 40% of households with Internet-connected TVs watch videos from Netflix, 17% watch YouTube (GOOG) videos, and 11% watch movies and TV shows via Hulu.