Yahoo Ranking Drop-Out

Owning multiple domains which point to the same site

[Quiche]

If I own URL-A and URL-B, and they both point through to www.mysite.com, should they both be returned in the organic search results, or would they be deduped.

For example, I bought URL-B to trial something which didn't work, so decided to redirect it back through to my main site in order to gain additional traffic for www.mysite.com. My problem is that URL-B keeps getting returned in the search results, with no sign of URL-A (the URL brand I promote in all my advertising).

What should I be doing here? Is this what you'd expect to happen? Why?