Molecular beam epitaxy (MBE) on patterned Si/AlN/Si(111) substrates was used to obtain regular arrays of uniform-size GaN nanowires (NWs). The silicon top layer has been patterned with e-beam lithography, resulting in uniform arrays of holes with different diameters (dh) and periods (P). While the NW length is almost insensitive to the array parameters, the diameter increases significantly with dh and P till it saturates at P values higher than 800 nm. A diffusion induced model was used to explain the experimental results with an effective diffusion length of the adatoms on the Si, estimated to be about 400 nm.