We study the Plancherel-Rotach asymptotics of four families of orthogonal polynomials: the Chen-Ismail polynomials,the Berg-Letessier-Valent polynomials,and the Conrad-Flajolet polynomials Ⅰ and Ⅱ.All these polynomials arise in indeterminate moment problems,and three of them are birth and death process polynomials with cubic or quartic rates.We employ a difference equation asymptotic technique due to Z.Wang and R.Wong.Our analysis leads to a conjecture about large degree behavior of polynomials orthogonal with respect to solutions of indeterminate moment problems.