If Wonder Woman from AA has an object (lets say heavy, for the heck of it), and uses her "tie up" ability to use incapacitate a close combat character... how does that work?

I was under the impression that you must use an object if making a close combat attack, and I can't think of any other figure in the game that possesses super strength and incap.

Does she incap for 2 damage instead of 0? Does she not use the object? Is the object wasted and it does 0 damage but adds tokens?

It would work like Gorgon and Maestro (Quake/Super Strength) or Controller (MC/SS). You get to make the attack without using the object.

The words "Wonder Woman" and "tie-up" gave me interesting mental images.

That is the purpose of the magic lasso. And you have to tell the truth. "No that is not a bannanna in my pocket. I am really happy to see you!"

"I haven't had this dream since I was 13."

That wouldn't be a true statement for some of us.

its no suprise they didnt help her, she was tied up, there was going to be a cat fight, they arent stepping in.

The relevant rule in this case can be found on the top of page 13 of the FF rulebook:
Incapacitate is an attack that will deal 0 damage, so the object is not used.
Note that the Stunning Blow feat changes this dynamic. Since the attack is no longer dealing 0 damage the object does get used. However, since Stunning Blow specifies that it deals damage equal to the printed damage value you won't get to use the damage bonus from the object.

Wonder Woman, tie-up, an object -- throw in a bottle of bourbon and you've got a pretty good weekend in Tijuana.

You fool!...the bottle of liquor IS the object. Sheesh.

I thought this had to do with bondage for some reason.

....

If you were to use Stunning Blow with Wonder Woman, dealing 4 clicks of damage and able to incap the target and an adjacent figure as well, would the 4 clicks of damage all go to the initial target, or could you split it between them?

I think by the wording of the power, the damage would all get dealt to the initial target, and the second figure would only get incapped, but I'd like to know for sure.

Geez, and now we've added the term "stunning blow" into the mix... this thread is just going downhill fast.