When an incorporation, discontinuance, or boundary adjustment is complete, the board shall supervise procedures necessary to carry out the proposal. In the case of an incorporation, the county commissioner of elections shall conduct an election for mayor and council of the city, who shall serve until their successors take office following the next regular city election. In the case of a discontinuance, the board shall publish two notices as provided in section 368.15 that it will receive and adjudicate claims against the discontinued city for a period of six months from the date of last notice, and shall cause necessary taxes to be levied against the property within the discontinued city to pay claims allowed. All records of a discontinued city shall be deposited with the county auditor of the county designated by the board. Any remaining balances shall be deposited in the county treasury where the former city was located. In the case of boundary adjustments, the proper city officials shall carry out procedures necessary to implement the proposal.