  A properly scaled critical Galton-Watson process converges to a continuous
state critical branching process $\xi(\cdot)$ as the number of initial
individuals tends to infinity.
  We extend this classical result by allowing for overlapping generations and
considering a wide class of population counts. The main result of the paper
establishes a convergence of the finite dimensional distributions for a scaled
vector of multiple population counts. The set of the limiting distributions is
conveniently represented in terms of integrals $(\int_0^y\xi(y-u)du^\gamma,
y\ge0)$ with a pertinent $\gamma\ge0$.
