  We investigate the long time behaviour of the one-dimensional ballistic
aggregation model that represents a sticky gas of N particles with random
initial positions and velocities, moving deterministically, and forming
aggregates when they collide. We obtain a closed formula for the stationary
measure of the system which allows us to analyze some remarkable features of
the final `fan' state. In particular, we identify universal properties which
are independent of the initial position and velocity distributions of the
particles. We study cluster distributions and derive exact results for extreme
value statistics (because of correlations these distributions do not belong to
the Gumbel-Frechet-Weibull universality classes). We also derive the energy
distribution in the final state. This model generates dynamically many
different scales and can be viewed as one of the simplest exactly solvable
model of N-body dissipative dynamics.
