We study Poisson customary and Poisson extended customary polynomials. We show that the sequence of codimensions {rn(V )}n¸1 of every extended customary space of variety V of Poisson algebras over an arbitrary field is either bounded by a polynomial or at least exponential. Furthermore, if this sequence is bounded by polynomial then there is a polynomial R(x) with rational coefficients such that rn(V ) = R(n) for all sufficiently large n. We present lower and upper bounds for the polynomials R(x) of an arbitrary fixed degree.
