  We discuss the late time evolution of the gravitational clustering in an
expanding universe, based on the nonlinear scaling relations (NSR) which
connect the nonlinear and linear two point correlation functions. The existence
of critical indices for the NSR suggests that the evolution may proceed towards
a universal profile which does not change its shape at late times. We begin by
clarifying the relation between the density profiles of the individual halo and
the slope of the correlation function and discuss the conditions under which
the slopes of the correlation function at the extreme nonlinear end can be
independent of the initial power spectrum. If the evolution should lead to a
profile which preserves the shape at late times, then the correlation function
should grow as $a^2$ [in a $\Omega=1$ universe] een at nonlinear scales. We
prove that such exact solutions do not exist; however, ther e exists a class of
solutions (``psuedo-linear profiles'', PLP's for short) which evolve as $a^2$
to a good approximation. It turns out that the PLP's are the correlation
functions which arise if the individual halos are assumed to be isothermal
spheres. They are also configurations of mass in which the nonlinear effects of
gravitational clustering is a minimum and hence can act as building blocks of
the nonlinear universe. We discuss the implicatios of this result.
