A "simulated amorphization and recrystallization" technique is employed to explore the structural modifications and epitaxial relationships, which evolve within a CeO2 thin-film when supported on yttrium-stabilized zirconia (YSZ). The epitaxial relationship identified within the CeO2/YSZ(111) system facilitates a reduction in the lattice misfit from ca. 6.1% (bulk misfit) to ca. 1% thereby, in part, stabilizing the system. In addition, edge dislocation networks and defects, including vacancies, substitutions, and interstitials evolve in both the CeO2 and the underlying YSZ to reduce further this residual misfit. Graphical techniques are employed to characterize and present, the epitaxial relationships and atomistic structure of the dislocation networks and defects that evolve within the system. Because experimentation is, at present, unable to explore the structural features that evolve within supported thin films with three-dimensional atomistic resolution, simulation provides an invaluable complement with which to study supported catalysts.