The nuclear spin-mediated quantum relaxation of ensembles of tunneling magnetic molecules causes a “hole” to appear in the distribution of internal fields in the system. The form of this hole and its time evolution, are studied using Monte Carlo simulations. It is shown that the line shape of the tunneling hole in a partially depolarized sample must have a Lorentzian line shape. The short-time half-width ξo in Fe8 crystals should be ∼E0, the half-width of the nuclear spin multiplet, but this result is not generally true. The Lorentzian hole line shape and the short-time √t relaxation in weakly polarized samples are both connected to a correlation time τde(ξ) for bias diffusion, whose inverse value also has a Lorentzian dependence on ξ.