  We consider a branching random walk on the lattice, where the branching rates
are given by an i.i.d. Pareto random potential. We show a very strong form of
intermittency, where with high probability most of the mass of the system is
concentrated in a single site with high potential. The analogous one-point
localization is already known for the parabolic Anderson model, which describes
the expected number of particles in the same system. In our case, we rely on
very fine estimates for the behaviour of particles near a good point. This
complements our earlier results that in the rescaled picture most of the mass
is concentrated on a small island.
