  We study solutions of three-term recurrence relations whose $N$-step transfer
matrices belong to the uniform Stolz class. In particular, we derive the first
order of their uniform asymptotics. For orthonormal polynomials we show more.
Namely, we find the constructive formula for the density of their orthogonality
measure in terms of Tur\'an determinants and we determine their exact
asymptotic behavior. We treat both bounded and unbounded cases in a uniform
manner.
