The authority of any county from which a portion is segregated under this chapter, for the collection of revenue within the boundaries of the portion segregated shall cease from the date upon which the two county courts, under the provisions of ORS § 202.210, base the settlement between such counties, and all assessments and levies made by the authority of the county from which such territory is segregated, by its officers in the lawful performance of their official duties, affecting any of the territories embraced in the boundaries of the new county or territory segregated by change in boundaries shall remain the same and shall be payable to, and be collected by, the lawful authorities of the new county or the lawful authorities of the county acquiring such new territory.