Unlike the one-dimensional case, when we deal with several complex variables, there exist entire one-to-one holomorphic maps with an identically equal to one jacobian, but with a non-dense range: the Fatou-Bieberbach maps (to simplify, we will call them Fatou-Bieberbach maps, even if there are not one-to-one). In Ref. [4], Gruman gave a sufficient density condition for a discrete set to be unavoidable and he constructed an explicit family of such sets $\ E_a , a \in \shadC ^*n \ $ . Analogeously to Nevanlinna theory, he showed that the Fatou-Bieberbach maps intersect these sets with the same asymptotic frequency for a outside a pluripolar set. In the present paper, we generalise these estimates to any discrete set E verifying the sufficient density condition by giving a lower and an upper bound for the pre-image of E by a Fatou-Bieberbach map F in terms of the growth of the function.