Heteroepitaxial thin films are widely used in a broad range of modern electronic devices, for example as the high-dielectric-constant (high-k ) gates in field effect transistors. In order to improve the crystal quality of epitaxial layers, researchers develop intricate and costly deposition processes. An alternative paradigm should involve deposition of the complex compounds that could exhibit unusual behavior and yield the high quality films by simple and industry-friendly processes. Successful search for the new complex compounds must employ combinatorial methods. In this publication, we demonstrate fabrication of composition spread materials libraries by Combi-PLD and their high-throughput characterization by two different XRD techniques. Generally, the composition spreads have polycrystalline, textured, and epitaxial areas of varied quality. We use statistical analysis to establish general guidelines for the epitaxial growth. Using the NiO-Co₃O₄-Mn₂O₃ system on SrTiO₃ as an example, we demonstrate that for the chemically inert interfaces lattice mismatch is the most important factor of the commensurate growth. For example, the rocksalt-perovskite interface requires the optimal lattice mismatch of ∼6.5%. Examination of the Y₂O₃-HfO₂-Al₂O₃ system on Si(100) revealed a narrow epitaxial area comprised of a new metastable crystal phase. Thus, stable epitaxial interface is attainable even for the chemically reactive boundaries. In addition to lattice mismatch, the high-quality heteroepitaxial film requires balancing the reaction with the outdiffusion of the reaction products away from the interface.