We establish basic properties of a sheaf graded algebras canonically associated to every relative affine scheme $$f:X\rightarrow S$$ endowed with an action the additive group $${\mathbb {G}}_{a,S}$$ over base or algebraic space S, which we call (relative) Rees algebra -action. In case varieties defined field characteristic zero, further {G}}_{a}$$ -action in terms its locally nilpotent derivati...