  At the LHC, the leading partons in the nuclei are expected to interact with
the maximal possible strength - black disk limit - up to transverse momenta of
the order of few GeV. We demonstrate that in this limit the densities of the
quark - gluon systems produced in the central AA collisions in the nucleus
fragmentation regions should exceed 300 GeV/fm^3 which is at least as high as
the densities discussed for the central region. Experimental signatures of such
a regime are also discussed.
