c. 1200, ounen, ahnen, "to possess, have; rule, be in command of, have authority over;" from Old English geagnian, from root agan "to have, to own" (see owe), and in part from the adjective own (q.v.). It became obsolete after c. 1300, but was revived early 17c., in part as a back-formation of owner (mid-14c.), which continued. From c. 1300 as "to acknowledge, concede, admit as a fact," said especially of things to one's disadvantage. To own up "make full confession" is from 1853. Related: Owned; owning.
"dominated, humiliatingly defeated, taken over," by 2001, "leetspeak" slang, probably from the common typographical mistake for owned (the -p- and -o- keys being adjacent on standard English keyboards) in the gamer slang sense "completely dominated by another" (in a contest).