It was founded in 1980 by Teri Lee, Jordin Kare, and Catherine Cook.
Like some other filk labels the name was a pun, in this case upon the idiom "off center" meaning eccentric, odd, or unusual -- all of which could be considered legitimate characterizations of filk music.
(Other filk labels have included Wail Songs, Unlikely Publications, and Random Factors, illustrating the style of self-deprecating humor common among these publishers.)
At an Interfilk auction at FilKONtario, a copy of Horse-Tamer's Daughter was sold for CA$400.00.
However, Off Centaur tapes are commonly considered "unobtainium" since few have been republished or re-created, and the best do tend to command collector prices.