We report on the numerical study of the relaxation rates of nuclear spins coupled through the hyperfine interaction to a two dimensional electron gas (2DEG) at magnetic fields corresponding to both fractional and integral Landau level (LL) fillings nu. The Hamiltonians of up to 20 interacting electrons are diagonalized exactly in the spherical geometry, neglecting finite layer width, disorder, and LL mixing. The spectral functions tau^-1(E) describing response of the 2DEG to the reversal of an

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... mbedded localized spin are calculated. In a (locally) incompressible nu=1 or 1/3 state, the finite Coulomb energy of short spin waves, together with the small nuclear Zeeman energy, prevent nuclear spin relaxation even in the limit of vanishing electron Zeeman energy E_Z. However, we find that the nuclear spins can couple to the internal excitations of mobile finite-size skyrmions that appear in the 2DEG at sufficiently low E_Z and at nu slightly different from 1 or 1/3. The experimentally observed dependence of nuclear spin relaxation rate on E_Z and nu is qualitatively explained in terms of the occurrence of skyrmions and antiskyrmions of various topological charge.