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1.
Area where one hangs out and/or resides. Origin is fuzy. Stomping or stompin' may refer to actual bushing out of entruders by stomping but today it is more of a reference to walking (stoping your feet). Hence, where one frequently hangs out and is seen. Everyone has stompin' grounds more or less.
"These are my old stomping grounds where is used to ride my motorcycle, frequently get hastled by the police and hang out in local bars"
by Toine December 01, 2005
 
2.
A dangerous territory or "turf" that one (or a few) is/are currently in possession of. Should a hostile enter the vicinity of the stomping grounds, they will be stomped upon.
"Where I lounge is my stomping grounds."

"The bitch-ass violated my stomping grounds so I curbed him."
by sux0r September 06, 2003