  We investigate the emergence of subdiffusive transport by obstruction in
continuum models for molecular crowding. While the underlying percolation
transition for the accessible space displays universal behavior, the dynamic
properties depend in a subtle non-universal way on the transport through narrow
channels. At the same time, the different universality classes are robust with
respect to introducing correlations in the obstacle matrix as we demonstrate
for quenched hard-sphere liquids as underlying structures. Our results confirm
that the microscopic dynamics can dominate the relaxational behavior even at
long times, in striking contrast to glassy dynamics.
