The consolidation charter shall provide for the delivery of services to specified areas of the county and of each consolidated city. The governing body of the consolidated government shall supervise the administration of the provision of services in each of the designated service areas and shall have the authority to determine the boundaries of the service areas. For each service provided by the consolidated government, the consolidated government shall assume the same statutory rights, powers, and duties relating to the provision of the service as if the county or the member city were itself providing the service to its citizens.