8 C.F.R. § 1003.4
In any case in which an appeal has been taken, the party taking the appeal may file a written withdrawal thereof with the office at which the notice of appeal was filed. If the record in the case has not been forwarded to the Board on appeal in accordance with § 1003.5 , the decision made in the case shall be final to the same extent as if no appeal had been taken. If the record has been forwarded on appeal, the withdrawal of the appeal shall be forwarded to the Board and, if no decision in the case has been made on the appeal, the record shall be returned and the initial decision shall be final to the same extent as if no appeal had been taken. If a decision on the appeal has been made by the Board in the case, further action shall be taken in accordance therewith. Departure from the United States of a person who is the subject of deportation proceedings subsequent to the taking of an appeal, but prior to a decision thereon, shall constitute a withdrawal of the appeal, and the initial decision in the case shall be final to the same extent as though no appeal had been taken. Departure from the United States of a person who is the subject of deportation or removal proceedings, except for arriving aliens as defined in § 1001.1(q) of this chapter, subsequent to the taking of an appeal, but prior to a decision thereon, shall constitute a withdrawal of the appeal, and the initial decision in the case shall be final to the same extent as though no appeal had been taken.
8 C.F.R. §1003.4