Abstract <p>In a recent author’s paper there was found the limit distribution of the properly normalized number of particles at a layer inside the propagation front of a supercritical catalytic branching random walk on an integer-lattice of any dimension. There was assumed that for the walk jump the Cramér condition is satisfied which means ‘‘lightness’’ of the distribution tails of the walk jump. The main achievement of the present work is extension of the mentioned result to the case of arbitrary set inside the front rather than a layer only. Thus, description of the density of particles population inside the front as time tends to infinity is now complete.</p>