In making applications for, and in expending, apportionments of funds under this chapter, a district acts as an agent of the state and all sites purchased and improved, all equipment purchased, and all buildings constructed, reconstructed, altered, or added to through the expenditure of funds apportioned under this chapter, are declared to be, and are, the property of the state. Upon the payment by the district of the amounts required to be paid by it to the state under this chapter, the board shall, in the name of the state, convey the property to the district.