  We study the geometric properties of polymixtures after a sudden quench in
temperature. We mimic these systems with the $q$-states Potts model on a square
lattice with and without weak quenched disorder, and their evolution with Monte
Carlo simulations with non-conserved order parameter. We analyze the
distribution of hull enclosed areas for different initial conditions and
compare our results with recent exact and numerical findings for $q=2$ (Ising)
case. Our results demonstrate the memory of the presence or absence of
long-range correlations in the initial state during the coarsening regime and
exhibit super-universality properties.
