  Using non-trivial mathematical properties of a class of nonlinear evolution
equations, we obtain the universal terms in the asymptotic expansion in
rapidity of the saturation scale and of the unintegrated gluon density from the
Balitsky-Kovchegov equation. These terms are independent of the initial
conditions and of the details of the equation. The last subasymptotic terms are
new results and complete the list of all possible universal contributions.
Universality is interpreted in a general qualitative picture of high energy
scattering, in which a scattering process corresponds to a tree structure
probed by a given source.
