  We present an ultra-low temperature study (down to T = 20 mK) of the nuclear
spin-lattice relaxation (SLR) in the 55Mn nuclei of the molecular magnet
Mn12-ac. The nuclear spins act as local probes for the electronic spin
fluctuations, due to thermal excitations and to tunnelling events. In the
quantum regime (below T = 0.75 K), the nuclear SLR becomes
temperature-independent and is driven by fluctuations of the cluster's
electronic spin due to the quantum tunnelling of magnetization in the ground
doublet. The quantitative analysis of the nuclear SLR shows that the presence
of fast-tunnelling molecules, combined with nuclear intercluster spin
diffusion, plays an important role in the relaxation process.
