  We use a non-linear characterization of orthonormal polynomials due to Saff
in order to show that the behavior of orthonormal polynomials is determined
only by its leading coefficient and its normalization. Several applications of
this equivalence are also discussed. One of our main results is that for
regular measures on the closed unit disk - including, but not limited to the
unit circle - one has ratio asymptotics along a sequence of asymptotic density
1.
