A developmental process, independent of morphogenetic (shape) change, that is required for the accessory nerve to attain its fully functional state. The spinal branch of this motor nerve innervates the trapezius and the sternocleidomastoid muscles. The cranial branch joins the vagus nerve and innervates the same targets as the vagus nerve. [ https://www.worldcat.org/search?q=bn%3A0838580343 GOC:dgh GOC:cls GOC:dph GOC:jid http://purl.obolibrary.org/obo/go/references/0000021 ]