On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters

We study the asymptotic zero distribution of Laguerre Ln(αn) and generalized Bessel Bn(αn) polynomials with the parameter αn varying in such a way that the limit of αn/n exists. Our approach is based on a non-hermitian orthogonality satisfied by these sequences of polynomials. In the cases that remain open we formulate the corresponding conjectures.