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We describe the general aspects of Monte Carlo Collision Generators suitablefor cosmic ray nucleon-Air and nuclei-Air interactions, including acceleratorand collider data. The problem of the extrapolation at 3 energy decades abovethe LHC of the main features of high energy collisions is discussed and undertheoretical and phenomenological assumptions, the properties of thelongitudinal and lateral development of giant extensive air showers simulatedwith the CORSIKA program are presented. The determination of the primary energynear $10^{20}$ eV is examined for different observables, total size, densitiesof charged particles interpolated at 600~m from shower core. The extensive airshower data collected around LHC energy is in better agreement with models oflarge multiplicities. Beyond this energy, the extrapolation carried assumingthe diquark breaking mechanism can change the classic conversion to primaryenergy and such circumstance can have consequences on the validity of the GZKcut off. In those conditions, we have simulated large and giant air showerstaking into account, in addition, new processes, such as diquark breaking, andtopological problems involving adequate structure functions for lateraldistributions, up to energies exceeding $10^{20}$ eV for P.AUGER and EUSOexperiments.

MULTIPLE PRODUCTION, TRANSPORT IN ATMOSPHERE AND DETECTION OF HIGH ENERGY COSMIC RAYS