Exceptional zeros of polynomials satisfying a three-term recurrence

Let Pm(z) be a sequence of polynomials satisfying the recurrence relation Pm(z)+B(z)Pm−1(z)+A(z)Pm−2(z)=0. Tran showed that with a suitable initial condition, the zeros of Pm(z) lie on a fixed explicit curve C on the complex plane. We study a more general initial condition in which we can count the finite number of zeros lying off C.