We have studied nucleation in superfluid He-3 across the A-B phase transition driven by a magnetic field, in a controllable environment at very low temperatures. Both B --> A and A --> B secondary nucleation appear to be governed by the survival of pockets of the new phase trapped at surfaces. We find that, at fields near B-AB, primary A --> B nucleation cannot be triggered by ionizing or neutron irradiation even at very high intensities; In our cell primary A --> B nucleation can only be triggered externally by mild mechanical shock.