2001 rules explain it, but it's rather complicated. Just do whatever seems to make the most sense.
With remote controls, just consider it like a pilot's chair that doesn't have to be attached to the vehicle. If you want to give it a minimum range you can, but keep in mind that your ultimate goal is for that remote to change hands as many times as possible.
I have to warn you, every time I put a remote control in an actual battle, the first team to get control of it immediately destroyed it in order to prevent the possibility of it falling into enemy hands. Every single time!
giving players remote controls, but not telling them what they do is the way to go!
Example: Santa (A.K.A. JEFFERY!) used the remote control to launch the Saturnalia tree missile into his enemies, Turning them into snowballs. someone else used their remote control, and drove a teensy little RC car, the third player used their remote, and got electrocuted by a snowman.
If you've got remote controled robot minifigs, then I would just treat them as normal minifigs, but there is another guy with a walkie-talkie/remote on the field. If this guy is killed, the robot he is controling stops working and can't do any thing until someone else picks up the remote. If the guy who picks up the remote is on the other team, then the robot is on the other team.