just for what it's worth, some documents got leaked recently, showing how next generation Apple devices will integrate projection, that says it all. You won't use a vertical screen anymore unless you want to play a game or watch a movie. Common office applications will be run on tablets usually, and if you still want to run them on a vertical screen (actual screen or projected image doesn't matter), you'll need something else than a mouse...
David I can already control my laptop from my iPod touch, using the touch screen as a touch pad ;-) ... as to the keyboard
used remotely, you'll have to use the one available on your tablet or your smartphone.