Video game console makers are finally thinking outside the box. At this year’s Electronics Entertainment Expo, each of the “big three” console makers have introduced features that move their content off the television.

Microsoft’s Xbox 360, Sony’s PlayStation and Nintendo’s Wii U are each trying to make their consoles more flexible entertainment hubs. All three have introduced new features at the industry’s biggest trade show that extend their content to smaller, more mobile screens. On Tuesday, Nintendo gave new details about the tablet controller for its Wii U, which can act as a portable screen within the home.

“It changes the way you enjoy your TV,” said Reggie Fils-Aime, Nintendo’s president for North America, in a presentation Tuesday at the Los Angeles expo.

Sony and Microsoft showed off their own extended features at the show on Monday. Sony announced that its handheld, the Vita, will be able to continue games started on the PlayStation 3. Microsoft announced Monday that some of its Xbox Live services will soon be available on the mobile devices that many consumers already own.

It’s about time. The explosion of smartphones and tablets has changed the way Americans consume entertainment: They are watching more video, browsing more Web pages and playing more games on the gadgets they carry with them all the time.

The trend has been good for the video gaming industry because it has popularized its products, but console makers are casting a wary eye at the growing mobile gaming market that Apple and Google have brought to a wider audience.

“The iPhone and iPad have trained the mainstream audience to play games everywhere that we go,” said Casey Lynch, editor in chief of IGN, a Web site devoted to video game news. “There’s this zeitgeist now of gaming.”

In the war for the living room, Microsoft is the only game maker to fully embrace the proliferation of screens. Those who subscribe to its Xbox Live service will be able to access their accounts from any smartphone or tablet through the new feature, called SmartGlass. Users will be able to view video or play some games right from Apple’s iPhones and iPads, Android phones and tablets, and, of course, Microsoft’s own mobile devices.

Sony, meanwhile, has added features that allow gamers to jump from device to device, but only if they’re made by Sony. Gamers who have Sony’s handheld Vita will be able to play games they’ve started on the PlayStation 3 — and vice versa — but the feature won’t work with other gadgets. Nintendo’s tablet controller is the most dependent on its main console, but players can move around the room with the controller.

Of the three approaches, Lynch said, Microsoft’s is the most sensible.

“It’s an elegant software solution — people understand how to use a smartphone or tablet to control other things,” he said.

Gaming, however, is just the beginning. The console makers have also built partnerships with video services such as Netflix and Hulu to keep customers logged into their services for hours at a time. Users of Microsoft’s Xbox 360 actually spend more time watching video or television on the console than they do playing games.

Building out non-gaming content, said Mike McGuire, a media analyst for Gartner, shows that console makers are moving to meet demand. “They’re extending the value of the platform by bringing in non-gaming content,” he said. “People still value the content, but they expect it to be portable and accessible on other devices.”

Staff writer Amrita Jayakumar contributed to this report.