Combinatorial substrate epitaxy (CSE) was used to study the orientation relationships (ORs) and polytypic stability of AEMnO(3) (AE = Ca, Sr) thin films grown on polycrystalline SrMnO3 and SrTiO3 substrates. SrMnO3 films with the stable four-layered hexagonal (4H) and metastable three-layered cubic (3C) structures were also grown on (111) and (100) SrTiO3 single crystal substrates, respectively. Electron backscatter diffraction data were used to determine the following ORs, which hold true regardless of the substrate surface orientation: (001)[100]4HSrMnO3||(001)[100]4HSrMnO3, (111)[11 over bar 0]3CCaMnO3||(001)[100]4HSrMnO3, and (001)[100]4HSrMnO3||(111)[11 over bar 0]3CSrTiO3. These are all simply the eutactic OR, which aligns the eutactic planes and directions; its ubiquity indicates that the interface energy is generally lower for the eutactic OR than for all other possible ORs. 3C SrMnO3 was found to grow only on very near (100) 3C SrTiO3 grains. This narrow range of epitaxial stabilization suggests that the penalties of higher interfacial and/or strain energies between polytypic perovskites adopting the eutactic OR are not significant enough to overcome the volumetric formation energy of the stable phase in these growth conditions, except for very special orientations.