(a) In case of a proposal to organize a park district as provided in subsection (a) of Section 2-2.1, the district shall be deemed organized if the proposal to organize the district receives the favorable vote of a majority of all votes cast on the question, and also receives the favorable vote of a majority of the votes cast within each of the existing park districts and in the territory, if any, not included in any existing park district. Thereupon the old park districts shall cease to exist, and the newly organized district shall succeed to all of their property and all their rights and obligations, including any bonded indebtedness.
     (b) In case of a proposal to reorganize a park district into 2 new park districts as provided in subsection (b) of Section 2-2.1, the district shall be deemed reorganized if the proposal to reorganize the park district receives the favorable vote of a majority of all votes cast within the park district to be so reorganized. Thereupon the old park district shall cease to exist, and the newly organized park districts shall succeed to all of its property and all of its rights and obligations, including any bonded indebtedness, as provided in Section 2-2.1.