  In this thesis, I describe in great detail the physics of the decay of any
Super-Heavy X particle (with masses up to the grand unification scale ~ 10^16
GeV and possibly beyond), and the computer code I developed to model this
process - which currently is the most complete available one. The general
framework for this work is the Minimal Supersymmetric Standard Model (MSSM).
The results are presented in the form of fragmentation functions of any
(s)particle of the MSSM into any final stable particle (proton, photon,
electron, three types of neutrino, lightest superparticle LSP) at a virtuality
Q = M_X, over a scaled energy range x = 2E/M_X in [10^{-13}, 1]. At very low x
values, color coherence effects have been taken into account through the
Modified Leading Log Approximation (MLLA). The whole process is explicitely
shown to conserve energy with a numerical accuracy up to a few part per mille,
which allows to make quantitative predictions for any N-body decay mode of any
X particle. I then apply the results to the old - and yet unsolved - problem of
Ultra High Energy Cosmic Rays (UHECRs). In particular, I provide quantitative
predictions of generic ``top-down'' models for the neutrino and neutralino
fluxes which could be observed in the next generation of detectors.
