Value distributions of derivatives of K-regular polynomial families

Let Ω ∈ C be a domain such that K := C \ Ω is compact and non-polar. Let (qk)k>0 be a sequence of polynomials with nk, the degree of qk satisfying nk →∞, and let (q(m) k )k denote the sequence of mth derivatives. We provide conditions which ensure that the preimages (q(m) k ) -1({a}) uniformly equidistribute on ∂Ω, as k→∞, for every a ∈ C and every m = 0, 1, . . . .