Using the approximate conformal invariance of QCD at high energies we consider a simple anti- de Sitter black disk model to describe saturation in deep inelastic scattering. Deep inside saturation the structure functions have the same power law scaling, F(T) similar to F(L) similar to x(-w), where w is related to the expansion rate of the black disk with energy. Furthermore, the ratio F(L)/F(T) is given by the universal value 1+3/3+w, independently of the target. For gamma* - gamma* scattering at high energies we obtain explicit expressions and ratios for the total cross sections of transverse and longitudinal photons in terms of the single parameter omega.