A Monte Carlo Potts model algorithm for single-phase normal grain growth is presented, which allows one to simulate the development of the microstructure of very large grain ensembles in three dimensions. The emphasis of the present work lies on the investigation of the relaxation process. Different initial grain structures characterized by different initial size distributions are subjected to grain growth via Monte Carlo simulation. The temporal development of 3D grain structures reaches independent of the initial size distribution, after an initial period of time, a quasi-stationary self-similar coarsening regime where all scaled size distribution functions collapse to the single universal, time independent size distribution f(x). The relaxation process to this universal self-similar state is studied by following the temporal development of quantities like the average grain size, the standard deviation of the grain size distribution and topological correlations.