  Branching random walks on multidimensional lattice with heavy tails and a
constant branching rate are considered. It is shown that under these conditions
(heavy tails and constant rate), the front propagates exponentially fast, but
the particles inside of the front are distributed very non-uniformly. The
particles exhibit intermittent behavior in a large part of the region behind
the front (i.e., the particles are concentrated only in very sparse spots
there). The zone of non-intermittency (were particles are distributed
relatively uniformly) extends with a power rate. This rate is found.
