Everything I've been able to find when Googling for this falls into one of these categories:
- it requires Jailbreaking;
- it's really just a way to display the iOS device's screen with AirPlay, and has nothing to do with controlling the screen;
- it's a remote support service that charges up the wazoo
I don't particularly want to pay $20 just to get around the fact that Apple doesn't see fit to support trackpads and mice in iOS. I can already connect my bluetooth keyboard to my iOS device, but I can't control the screen (as though I were touching the screen itself, without actually raising my arm up to monitor height, where my iOS device is mounted).
I do not need remote control—that is, control from a remote network—but if I can gain control of the screen using something designed for remote control, that's fine.