The epitaxial growth of the methoxy functionalized para-quaterphenylene (MOP4) on the (001) faces of the alkali halides NaCl and KCl and on glass is investigated by a combination of low energy electron diffraction (LEED), polarized light microscopy (PLM), atomic force microscopy (AFM), and X-ray diffraction (XRD). Both domains from upright molecules as well as fiber-like crystallites from lying molecules form. Neither a wetting layer from lying molecules nor widespread epitaxial fiber growth on the substrates is detected. Our results focus on the upright standing molecules, which condense into a thin film phase with an enlarged layer spacing compared to the bulk phase.