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We consider a large spin \bf S in the magnetic field parallel to the uniaxialcrystal field, interacting with N >> 1 nuclear spins \bf I_i via Hamiltonian\cal H = -DS_z^2 - H_zS_z+ A{\bf S}\cdot \sum_{i=1}^N {\bf I}_i with A << D, attemperature T. Tunneling splittings and the selection rules for the resonantvalues of H_z are obtained perturbatively. The quantum coherence exists at T <<ASI while at T >= ASI the coherence is destroyed and the relaxation of \bf S isdescribed by a stretched dependence which can be close to log t under certainconditions. Relevance to Mn-12 acetate is discussed.Comment: 5 PR pages, 4 figures, submitted to PR

Tunneling of a large spin via hyperfine interactions