Vancouver
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1998 - Artem Chubarov (Burke had just been hired a week before, so it's tough to imagine he had a ton of input on the draft process)
1999 - traded to Avs for coach Marc Crawford
2000 - Had two picks, traded own pick for 2001 pick, traded another for Devils prospect Vadim Sharifijanov
2001 - Had three picks, traded for Drake Berehowsky, traded with Adrian Aucoin for Dan Cloutier, traded for Alex Auld
2002 - Had two picks, selected Kirill Kolstov and Denis Grot
2003 - Marc-Andre Bernier
2004 - Traded for Johan Hedberg
Anaheim
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2005 - Had two picks, drafted Brendan Mikkelson with one, traded the other for Todd Fedoruk
2006 - Had two picks, drafted Bryce Swan with one, traded the other for Jeff Friesen
2007 - Had three picks, drafted Eric Tangradi with one they got by trading down, traded for George Parros (with pick they got for Vitali Vishnevski), traded their own pick in a package for coach Randy Carlyle
2008 - Used own pick in the Pronger trade, traded down twice for picks #35 and #39 and got Nic Deschamps and Eric O'Dell.
2009 - Traded for Brian Sutherby in 2007
Toronto
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2009 - Acquired two picks via trade, drafted Kenny Ryan and Jesse Blacker
2010 - Reacquired then used own 2nd in the Phil Kessel trade, acquired a pick for Jimmy Hayes and drafted Brad Ross
Obviously not the greatest array of talent brought in, but the teams getting those 2nd rounders generally didn't draft guys who were much better.