Most smartphones now have sensors that are around or above 4K in resolution, but not many of them claim to be able to capture 4K video. Samsung's Galaxy Note III looks set to do this, though, according to various rumours
You can see why Samsung might want to do this: they sell 4K televisions, and, sooner than most people expect, all televisions on sale will be 4K: well before there is much 4K content available to consumers. So what better way to redress this unbalance than putting the ability to capture 4K into smartphones?
In an uninformed consumer's mind, it's a simple equation: 4K into the camera = 4K out of the television. But it's not so simple.
Have you ever seen those big, heavy glass things they put on the front of cameras? You know, lenses? They're big and heavy for a reason. You need lots of light and to be able to manipulate it precisely. You can't do this with smartphone lenses. You can take pictures that might be acceptable if you haven't got anything better, but no-one is likely to prefer or even mistake iPhone or Galaxy footage over XDCAM, F55 or Alexa. More truthfully, we should say no-one is going to prefer the performance of a smartphone's lens over that of a professional piece of glass that costs as much as a car.
I have never seen "HD" footage from a phone that looked like it was really HD - although it's kind of surprising just how good it can look!
So, good luck with your 4K smartphone. It will probably give remarkably good pictures, but (and I'm prepared to eat my words when we actually see one) if you measure the actual resolving power of the phone's sensor/lens/compression combination, it isn't going to be 4K, however many pixels it claims to have.