See the modern Wiktionary entry at abbacy
A′bbacy. n. s. [Lat. abbatia.] The rights or privileges of an abbot. See Abbey.
According to Felinus, an abbacy is the dignity itself, since an abbot is a term or word of dignity, and not of office; and, therefore, even a secular person, who has the care of souls, is sometimes, in the canon law, also stiled an abbot.Ayliffe's Parergon Juris Canonici.