The Division of Child Protective Services may utilize services of other child welfare agencies and allocate and turn over unto such agencies, operating within this State and rendering child welfare services, any portion of funds appropriated for the purposes of this chapter and as may from time to time be deemed necessary, proper and expedient for the supervision, care, custody, board and placement of dependent and neglected children. If in the judgment of the Division such payments are necessary, proper and expedient for the care of the child, these allocations and payments may be continued to the said agency for children who were dependent or neglected, but who have been legally adopted.