  We consider a continuous-time symmetric branching random walk on the
$d$-dimensional lattice, $d\ge 1$, and assume that at the initial moment there
is one particle at every lattice point. Moreover, we assume that the underlying
random walk has a finite variance of jumps and the reproduction law is
described by a critical Bienamye-Galton-Watson process at every lattice point.
We study the structure of the particle subpopulation generated by the initial
particle situated at a lattice point $x$. We answer why vanishing of the
majority of subpopulations does not affect the convergence to the steady state
and leads to clusterization for lattice dimensions $d=1$ and $d=2$.
