Split Supersymmetry at the Logarithmic Test of Future Colliders.

We consider a large number of pair production processes at future colliders (LHC, ILC) for values of the c.m. energy in the TeV range, where a logarithmic expansion of Sudakov kind would provide a reliable description of Split supersymmetric electroweak effects. We calculate all the leading and next to leading terms of the expansions, that would differ drastically in the considered domain from those of an extreme "light" scenario. We imagine then two possible competitive future situations, at LHC and at ILC, where the determination of the energy dependence of the cross sections of certain processes could reveal a "signal" of the correct supersymmetric scheme.