If a draw effect is canceled (i.e. King's Landing) do the "would have been drawn" cards apply to the player's draw cap?

I'd say no because they HAVE NOT BEEN DRAWN. The rules say you may draw only 3 additional cards.

Correct. The way that the draw cap is worded, cards have to physically end up in your hand before they count against it. That's because the draw cap is checked as the effect resolves (which is what allows you to trigger a "draw 3 cards" effect, even if you have already drawn 2 that round, and get just 1 of the 3 cards).

This is different from pretty much every other limit in the game, particularly limits on effects themselves (eg: "limit once per phase," etc.). Those limits are checked when they are initiated. So even if the effect is canceled, it counts against the limit of how many times you can trigger the effect.

Thanks. That's what I thought, but I wanted some verification.