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1.
means leave me some of that cigarette.

It means please give me your cigarette after you've smoked half of it

means let me have a few puffs of your cigarette
"Bust me down on that stog."
by Atul April 19, 2006
 
2.
A question you might ask a close friend when that friend pulls out a cigarette if you would like to share a cig with that friend.
- a couple second after friends pulls a cigarette out of his poket-

"Hey bro, you gonna bust me down?"
by Josh Harris (slang creator) April 17, 2007