N.Y. Jud. Law § 71
From all the justices elected to the supreme court the governor shall designate those who shall constitute the appellate division in each department, and he shall designate the presiding justice thereof, who shall act as such during his term of office, and shall be a resident of the department. The other justices shall be designated for terms of five years, or the unexpired portions of their respective terms of office, if less than five years. From time to time, as the terms of such designations expire, or vacancies occur, the governor shall make new designations. He may also, on request of any appellate division, make temporary designations in case of the absence or inability to act of any justice in such appellate division, for service during such absence or inability to act. In case any appellate division shall certify to the governor that one or more additional justices are needed for the speedy disposition of the business before it, the governor may designate an additional justice or justices; but when the need for such additional justice or justices shall no longer exist, the appellate division shall so certify to the governor and thereupon service under such designation or designations shall cease. A majority of the justices designated to sit in any appellate division shall at all times be residents of the department. A designation of a justice of the appellate division of the supreme court must be in writing, and filed in the office of court administration.
N.Y. Jud. Law § 71