Notwithstanding any provisions of any other statute, the authority in conjunction with the commissioner of parks of the city or his successor, the commissioner of parks and recreation, and with the approval of the board of estimate of such city and with the separate approval of the mayor thereof, is hereby authorized to select sites in the boroughs of the Bronx and Queens of the city for the Whitestone bridge project and parkways connecting therewith, which sites may be in or through existing public parks, and to select sites for new public parks contiguous to such project or contiguous to the roads, streets, parkways or avenues connecting with such project. A site or sites may be selected for any or all of the aforementioned purposes and thereafter the use thereof shall be allocated by the commissioner of parks and recreation as herein provided. The property so selected solely for such project, not already owned by the city, shall be acquired at the sole expense of the authority in the manner provided for under this title. The property so selected solely for new public parks shall be acquired by the city at its sole expense. The cost of the property so selected for such project, combined with any other aforementioned purposes the use of which is to be thereafter determined, shall be divided between the city and the authority as may be determined by a contract or contracts hereby authorized to be entered into between the city and the authority, subject to the approval of the board of estimate of the city. So much of the sites so selected and acquired or such easements or rights of way therein as may be necessary or convenient for the corporate purposes of the authority may be assigned by the commissioner of parks and recreation of the city to the authority for its use so long as its corporate existence shall continue.