The department of lands shall have power:
(1) To exercise, under the general control and supervision of the state board of land commissioners all the rights, powers and duties vested by law in the state board of land commissioners, except the supervision of public investments, the administration of the Carey Act and the administration of chapter 26 of title 42, Idaho Code.
(2) To exercise all the rights, powers and duties of the register of the state board of land commissioners except such as have been transferred.
(3) To organize a central land records unit within the department for the purpose of establishing and maintaining an inventory and plat of all lands owned, leased, or held in trust by the state or any of its agencies, departments, institutions or instrumentalities, and to require any such agency, department, institution or instrumentality to file with the unit for recordation and platting any instrument by which the state or any such agency, department, institution or instrumentality acquires or disposes of title to real property or an estate therein.