  Within the framework of hierarchical clustering we show that a simple
Press-Schechter-like approximation, based on spherical dynamics, provides a
good estimate of the evolution of the density field in the quasi-linear regime
up to $\Sigma \sim 1$. Moreover, it allows one to recover the exact series of
the cumulants of the probability distribution of the density contrast in the
limit $\Sigma \to 0$ which sheds some light on the rigorous result and on
``filtering''. We also obtain similar results for the divergence of the
velocity field.
  Next, we extend this prescription to the highly non-linear regime, using a
stable-clustering approximation. Then we recover a specific scaling of the
counts-in-cells which is indeed seen in numerical simulations, over a
well-defined range. To this order we also introduce an explicit treatment of
the behaviour of underdensities, which takes care of the normalization and is
linked to the low-density bubbles and the walls one can see in numerical
simulations. We compare this to a 1-dimensional adhesion model, and we present
the consequences of our prescription for the power-law tail and the cutoff of
the density distribution.
