I actually have a couple of fond memories of Brian Burke at the 2010 Draft.
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In round 3, I spotted Burke/Nonis having a conversation with a very animated Dean Lombardi. Since it was by Central Registry, I thought a big trade (Tomas Kaberle) was about to go down. But it ended up being a more insignificant one. LA traded a 3rd rounder (#79) to Toronto for a 2012 3rd. Through some other intel, I think LA wanted to draft Radko Gudas who they had at their previous summer prospect camp as an undrafted invite. Gudas had a good year in the WHL afterwards. Tampa took him #66.
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And then in the fourth round, I spotted Brian Burke walking table to table shopping Toronto's 4th rounder (#112). Eventually he found a taker with Washington who traded up for Philipp Grubauer.
Might have been a 'you had to be there' moment, but there was something comical about Burke walking up to a table and asking "you want my 4th?", getting turned down, and proceeding to the next table.