  We analyze the subsystem size scaling of the entanglement entropy of a
non-ergodic pure state that can be described by a multi-parametric Gaussian
ensemble of complex matrices in a bipartite basis. Our analysis indicates, for
a given set of global constraints, the existence of infinite number of
universality classes of local complexity, characterized by the complexity
parameter, for which the entanglement entropy reveals a universal scaling with
subsystem size. A rescaling of the complexity parameter helps us to identify
the critical regime for the entanglement entropy of a broad range of pure
non-ergodic states.
