All territory comprised within cities of the second class shall be a part of the county institution district of the county in which such city is located. All city institution districts in cities of the second class are hereby abolished. The property, real and personal, of each existing city institution district in each city of the second class, and the property, real and personal, of each city of the second class used for city institution district purposes, on the effective date of these amendments, is hereby transferred to and vested in the county institution district of the county wherein the city of the second class is located. All indebtedness of any city of the second class, whether current or bonded incurred in the acquisition of any of such property or for any other city institution district purpose, shall continue the debt and obligation of such city of the second class and shall be paid by it. All the powers and duties of cities of the second class, in connection with administering the affairs of the city institution district, are hereby transferred to the county institution district of the county in which such city is located.