  We provide results of uniqueness for holomorphic functions in the Nevanlinna
class bridging those previously obtained by Hayman and Lyubarskii-Seip. Namely,
we propose certain classes of hyperbolically separated sequences in the disk,
in terms of the rate of non-tangential accumulation to the boundary (the
endpoints of this spectrum of classes being respectively the sequences with a
non-tangential cluster set of positive measure, and the sequences violating the
Blaschke condition); and for each of those classes, we give a critical
condition of radial decrease on the modulus which will force a Nevanlinna class
function to vanish identically.
