The growth of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA) on the Ga-polar GaN(0 0 0 1) surface has been studied by x-ray photoelectron spectroscopy (XPS), spot profile analysis low-energy electron diffraction (SPA-LEED), near edge x-ray absorption fine structure (NEXAFS), and scanning tunneling microscopy (STM). The stoichiometric ratios derived from XPS indicate that the molecules remain intact upon adsorption on the surface. Furthermore, no chemical shifts can be observed in the C 1s and O 1s core levels with progressing deposition of PTCDA, suggesting none or only weak interactions between the molecules and the substrate. NEXAFS data indicate the PTCDA molecules being oriented with their molecular plane parallel to the surface. High-resolution STM shows PTCDA islands of irregular shape on the sub-micron scale, and together with corresponding SPA-LEED data reveals a lateral ordering of the molecules that is compatible with the presence of (1 0 2) oriented PTCDA nano-crystals. SPA-LEED moreover clearly shows the presence of homogeneously distributed rotational domains of two-dimensionally isotropic PTCDA.