Continuum (and stuff like it) is surely the future of personal computing. You'll have one personal pooter, always in your pocket, presumably with data backed up to the cloud, and you'll just dock it or connect it to screens networks and input devices as you go about your day. Phones are now as powerful computers as normal laptops were 5-10 years ago, and people worked on them perfectly easily.
How long it takes for the technology to make this a seamless process is anyone's guess. With enough investment and industry cooperation, we ought to be able to do it this year. In reality I can't see it being more than 5-10 years away.