This paper discusses the growth of Mg-doped GaN samples using a modified Molecular Beam Epitaxy (MBE) method. Our results suggest that the dopant is incorporated from a surface population maintained by the incident Mg flux by a rapid diffusion mechanism. It follows that the chemical concentration will increase with time of growth and that the p-doping level will also increase progressively with film thickness for a given Mg flux. Increasing the Mg flux to the surface results at first in a higher doping density, but this saturates when the Mg surface concentration reaches a finite value.