There is already a large variety of applications on the consumer market made of thin films of organic semiconducting materials. Therefore, it is crucial to understand the formation mechanisms of such organic films. Here, thin films of the aromatic rod-like molecule Para-hexaphenyl (6P) were grown by organic molecular beam epitaxy under ultra-high vacuum conditions. For these experiments, Ar+-bombarded mica and silicon dioxide (SiO2) were used as amorphous substrates. 6P tends to build mounds of nearly upright standing molecules on this kind of substrates. The growth morphology of these thin films was investigated by various ex- and in-situ atomic force microscopy techniques (AFM). One important parameter in nucleation of thin-film growth is the critical nucleus size i*. The analysis of the experiments reveals that the calculated values for i* from rate theory, island-size scaling, and capture-zone scaling (using the generalized Wigner surmise) are in good agreement with each other. 6P on ion-bombarded mica and on SiO2 can exhibit a post-nucleation with a dewetting by virtue of the exposure to air, most probably because of water co-adsorption. After growth, short annealing of 5 to 10 minutes up to a substrate temperature of 423 K was applied to the 6P thin films. AFM phase mode investigations yield that islands shrink, but something remains or changes the surface at the position of the former islands. Kelvin probe force microscopy reveals a change in the contact potential difference at these positions in comparison with positions at remaining 6P islands or pure SiO2. Further, 6P was deposited under a grazing incidence at angles between 70° and 85° with respect to the substrate's surface normal. Steering effects, which are present in inorganic growth under grazing incidence, were not observed for organic thin films of 6P on SiO2. However, there is an evidence of a slight change in the fractal dimension of the resulting 6P islands. Finally, the nucleation of elongated hexagonal islands in subsequent layers was investigated by AFM and simulations using empirical force-fields (EFF) together with molecular dynamics (MD) simulations were performed. The preferable inner angles of the hexagonal islands are (104±2)° and (126±2)°. EFF simulations result in an octagonal structure as an equilibrium shape of the 6P single crystal and MD simulations explain the formation of a hexagonal structure because the 6P molecules have a higher sticking probability at the [10] facet.