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2.
Behaviour outside the realms of normal, with respect to the individual.

To do one's own thing.

To 'give the birdie' to the world and make a concerted effort to annoy / piss off / offend as many people as possible in a given timeframe.
John: Er... is Calvin off on one?
James: Nope - he usually chases pigeons on his lunchbreak.

James: Woah - does Miranda usually dance on tables whilst inebriated, sans underwear??
John: Nope - she's off on one.
by mr. duffy March 07, 2010
 
1.
To behave in an extreme, inappropriate manner in response to provocation.
When he heard he just went 'off on one' and wouldnt stop ranting for several hours.
by terminal.eight March 05, 2006