  A classical spin network consists of a ribbon graph (i.e., an abstract graph
with a cyclic ordering of the vertices around each edge) and an admissible
coloring of its edges by natural numbers. The standard evaluation of a spin
network is an integer number. In a previous paper, we proved an existence
theorem for the asymptotics of the standard evaluation of an arbitrary
classical spin network when the coloring of its edges are scaled by a large
natural number. In the present paper, we extend the results to the case of an
evaluation of quantum spin networks of arbitrary valency at a fixed root of
unity. As in the classical case, our proofs use the theory of $G$-functions of
Andr\'e, together with some new results concerning holonomic and $q$-holonomic
sequences of Wilf-Zeilberger.
