  In this paper we present the results of numerical studies of the JIMWLK and
BK equations with a particular emphasis on the universal scaling properties and
phase space structure involved. The results are valid for near zero impact
parameter in DIS. We demonstrate IR safety due to the occurrence of a rapidity
dependent saturation scale Q_s(\tau). Within the set of initial conditions
chosen both JIMWLK and BK equations show remarkable agreement. We point out the
crucial importance of running coupling corrections to obtain consistency in the
UV. Despite the scale breaking induced by the running coupling we find that
evolution drives correlators towards an asymptotic form with near scaling
properties. We discuss asymptotic features of the evolution, such as the \tau-
and A-dependence of Q_s away from the initial condition.
