Can a linear power supply be used for multiple devices?

“...when fed it's rated voltage, will consume no more current than specified, regardless of how much is available.”

Thanks erik. This answers the question for me. My comment about the device getting too warm was related to a battery charging system (cordless screwdriver) which you also addressed.

"So, if you have two 12V devices, and each needs 1 Amp, then your power supply needs to put out 12V at 2A or more."

This topic comes up often and I'm still a little confused. You seem to imply that you can feed more current than what's spec'd on the wall wart. So are you saying if a device has a 0.5A @ 12V (6 Watts) wall wart, you can supply it with 1A @ 12V (12 Watts) without issues?  Last time I tried this the device got too warm to touch. I thought the LPS needs to match both the V and the A (or mA) of the wall wart its replacing.