I did this about six months ago and again about three months ago. I asked only for cards in return from teams I collect or a card or two off my key wants (GQ framed paper, Kimball Champions, Heritage 2011, 1976 or 1978 Topps, for example).
As a result of previous junk sales, I'm tapped thin on a few teams so if you want these teams: Dodgers, Cardinals, Blue Jays, Braves, Mets, Yankees, Phillies, Royals - I'm either completely out or fairly low but might be able to rustle up a couple of dozen. Also, I only have a handful of cards from the newer, expansion teams. Happy to send them, but there aren't many.
But for certain other teams I have anywhere from 40 to 100 cards to send.
I also have a solid stockpile of Reds and Tigers to send as a result of earlier junk for junk trades, so if anyone wants a healthy stock from those teams, let me know. Cubs too, I think.
And, if you'd like to expand the deal to include cards beyond "junk" feel free to make some suggestions.
P.S. I haven't forgotten about the contest and I'm keeping track of the entrants so far. I'll have at least one more way soon to get another entry.