Thermally stimulated depolarization current (TSDC) of acceptor (Mg)-doped BaTiO3 ceramics was analyzed for submicrometer fine grain specimens. For a fixed condition of polarization field (E-P) and polarization time (t(P)), the TSDC associated with an oxygen vacancy (V-o) relaxation showed two peaks with relaxation temperatures (T-m) under low polarization temperature (T-P) conditions. It is inferred that the TSDC peak of the lower T-m is due to the relaxation of a V-o distributed space charge within a grain and has a short relaxation time constant (tau(0)), and the higher T-m is due to the long-range relaxation across grain boundaries with a larger time constant, tau(0). The onset condition for resistance degradation can be correlated with the breaking point of T-P, at which the TSDC peak changes from in-grain relaxation to across-grain boundary relaxation. The breaking point of T-P and the time to degradation systematically decreased with the increase of acceptor concentration. Such behavior can be correlated with the decrease of T-P, T-m, tau(0), and little change of activation energy of V-o relaxation, which is due to the increase of V-o concentration.