  We study the development of gravitational instability in the strongly
non-linear regime. For this purpose we use a number of statistical indicators
such as filamentary statistics, spectrum of overdense/underdense regions and
the void probability function, each of which probes a particular aspect of
gravitational clustering. We use these statistical indicators to discriminate
between different approximations to gravitational instability which we test
against N-body simulations. The approximations which we test are, the truncated
Zel'dovich approximation (TZ), the adhesion model (AM), and the frozen flow
(FF) and linear potential (LP) approximations. Of these we find that FF and LP
break down relatively early, soon after the non-linear length scale exceeds
$R_*$ -- the mean distance between peaks of the gravitational potential. The
reason for this break down is easy to understand, particles in FF are
constrained to follow the streamlines of the initial velocity field. Shell
crossing is absent in this case and structure gradually freezes as particles
begin to collect near minima of the gravitational potential. In LP particles
follow the lines of force of the primordial potential, oscillating about its
minima at late times when the non-linear length scale $k_{\rm NL}^{-1}\simeq
R_*$. Unlike FF and LP the adhesion model (and to some extent TZ) continues to
give accurate results even at late times when $k_{\rm NL}^{-1} \ge R_*$. This
is because both AM and TZ use
