We demonstrate spontaneous growth of a high density of self-organized, oriented, and epitaxial GaN low-dimensional nanostructures on Al2O3(0001) by sheer kinetic control without involving lithography, catalysts, buffer layers, or any surface pretreatment and consequently reducing process steps. GaN thin films grown by plasma assisted-molecular beam epitaxy (PA-MBE) form wurtzite GaN as a nanowall hexagonal network of flat 2-D films. In a narrow parametric window, 1-D nanocolumns of high density (1 × 108 cm–2) with excellent structural and optical properties are observed. The reduced adatom diffusion in the high nitrogen rich conditions is proposed to cause supersaturation and nucleation at edge and screw dislocations, forming nanowalls and nanocolumns.