  We constrain mass, lifetime and contribution of a very slowly decaying Ultra
Heavy Dark Matter (UHDM) by simulating the cosmological evolution of its
remnants. Most of interactions which participate in energy dissipation are
included in the numerical solution of the Boltzmann equation. Cross-sections
are calculated either analytically or by using PYTHIA Monte Carlo program. This
paper describes in detail our simulation. To show the importance of the
distribution of matter in constraining WIMPZILLA characteristics, we consider
two extreme cases: a homogeneous universe, and a local halo with uniform
distribution. We show that in a homogeneous universe, the decay of UHDM with a
mass \sim 10^15 GeV and a lifetime \sim a few times \tau_0 the age of the
Universe, can not explain the flux of observed Ultra High Energy Cosmic Rays
(UHECRs). This shows the importance of nearby sources, notably galactic halo.
In a uniform clump with an over-density of \sim 200 extended to 100 kpc or
more, the lifetime must be \sim 10 - 100 \tau_0 or the contribution in the DM
must be proportionally smaller. We also compare our calculation with observed
gamma-rays at E \sim 10^11 eV by EGRET and CASA-MIA limit at E \sim 10^15 eV.
They are compatible with a UHDM with relatively short lifetime.
