We have identified crystal growth conditions in plasma-assisted molecular beam epitaxy (PAMBE) that leads to spontaneous formation of GaN nanostructure like nanowalls, nanotubes, and nanorods on c-plane sapphire. We have grown GaN on c-plane Al 2 O 3 substrate at temperatures 630, 680 and 780 1C. The rf plasma forward power W f ΒΌ375 W and nitrogen content $ 4.5 sccm was kept constant for all growths. The micro-structural and structural information is extracted by high-resolution X-ray diffractometry (HRXRD) and reflection high-energy electron diffraction (RHEED). For studying optical properties of nanostructures photoluminescence (PL) spectroscopy is employed. X-ray diffraction study shows that the formed GaN nanostructures are of high crystalline quality and also well aligned along the symmetric (0 0 0 2), (0 0 0 4) peaks of wurtzite GaN. The morphology of grown nanostructures is characterized by field emission scanning electron microscopy (FE-SEM). The morphology of GaN nanostructures in a plan view of FE-SEM images shows that the nanostructures seem to be formed out of a well separated matrix layer containing deep faceted holes. The shape of fully strain relaxed nanostructure diameter varies from 50 to 200 nm at different temperatures. In this study we have optimized the deposition conditions needed to form self-assembled nanostructures of various sizes and assembly. The growth controlled by kinetics thus enables us to form spontaneous GaN nanostructures without use of catalysts or buffer layers.