  We describe the general aspects of Monte Carlo Collision Generators suitable
for cosmic ray nucleon-Air and nuclei-Air interactions, including accelerator
and collider data. The problem of the extrapolation at 3 energy decades above
the LHC of the main features of high energy collisions is discussed and under
theoretical and phenomenological assumptions, the properties of the
longitudinal and lateral development of giant extensive air showers simulated
with the CORSIKA program are presented. The determination of the primary energy
near $10^{20}$ eV is examined for different observables, total size, densities
of charged particles interpolated at 600~m from shower core. The extensive air
shower data collected around LHC energy is in better agreement with models of
large multiplicities. Beyond this energy, the extrapolation carried assuming
the diquark breaking mechanism can change the classic conversion to primary
energy and such circumstance can have consequences on the validity of the GZK
cut off. In those conditions, we have simulated large and giant air showers
taking into account, in addition, new processes, such as diquark breaking, and
topological problems involving adequate structure functions for lateral
distributions, up to energies exceeding $10^{20}$ eV for P.AUGER and EUSO
experiments.
