In this paper, we prove that every lax generalized Veronesean embedding of the Hermitian unital U of PG(2, L), L a quadratic extension of the field K and |K| ≥ 3, in a PG(d, F), with F any field and d ≥ 7, such that disjoint blocks span disjoint subspaces, is the standard Veronesean embedding in a subgeometry PG(7, K ) of PG(7, F) (and d = 7) or it consists of the projection from a point p ∈ U of U \ {p} from a subgeometry PG(7, K ) of PG(7, F) into a hyperplane PG(6, K ). In order to do so, when |K| > 3 we strongly use the linear representation of the affine part of U (the line at infinity being secant) as the affine part of the generalized quadrangle Q(4, K) (the solid at infinity being non-singular); when |K| = 3, we use the connection of U with the generalized hexagon of order 2
