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We investigate acceptor and donor states in GaN nanocrystals doped with a single substitutional impurity. Quantum dots (QDs) of zinc-blende structure and spherical shape are considered with radius ranging from 4.5 to 67.7 Å. The size-dependent energy spectra are calculated within the sp3d5s* tight-binding model, which yields a good agreement with the confinement-induced blueshifts observed in undoped QDs. The computed binding energy is strongly enhanced with respect to the experimental bulk value when the dopant is placed at the center of the smallest QDs. It decreases with increasing QD size following a scaling law that extrapolates to the bulk limit. In order to estimate the degree of localization of the bound carriers, we analyze their wave functions and average radii. The resulting physical picture points to a highly localized acceptor hole, mostly distributed over the nearest-neighbor anion shell, and a much more extended donor electron. We also study off-center impurities in intermediate-sized QDs. The acceptor binding energy is approximately independent of the dopant position unless it is placed within a surface shell of thickness of the order of the bulk Bohr radius, where the ionization energy abruptly drops. On the contrary, the donor binding energy gradually decreases as the impurity is moved away from the center toward the QD surface. [ABSTRACT FROM AUTHOR]