[MunchkinMan]

You are correct. Giving away an Item is no different than trading it for nothing in return, so you can't do it while you are in combat, or the other player is in combat. Also, you can trade your extra Big Item in that circumstance, but if no one is willing to trade, then you're stuck with selling it or giving it to the lowest Level player who can take it. The main issue that we're concerned with is making sure that you get rid of it in a legal way before you end up having to discard it.

A useful addition: You can't play a second Big Item to put yourself in this situation. You have to come by it by having lost whatever allowed you the extra Big Item(s) in the first place. That doesn't mean, however, that you couldn't be a Dwarf, play an extra Big Item from your hand, then discard your Dwarf Race to force yourself into that situation, but now I'm giving away the farm. . . ;-)