If, subsequent to the dissolution of a park district under this section, a new park district, the greater portion of which was contained within the area of the dissolved park district, is organized as the result of a petition filed within one (1) year after such dissolution, all of the parks and other property that vested in the school district as a result of such dissolution shall thereupon vest in the newly organized park district, and the newly organized park district shall succeed to all of the outstanding rights and obligations of the dissolved district, and the power and authority of the trustees of the schools or the school district with respect to the affairs of the dissolved district shall terminate.