  We perform Monte Carlo simulations of diffusive shock acceleration at highly
relativistic oblique shock waves. High upstream flow Lorentz gamma factors are
used, which are relevant to models of ultra relativistic particle shock
acceleration in Active Galactic Nuclei (AGN) central engines and relativistic
jets and Gamma Ray Burst (GRB) fireballs. We investigate numerically the
acceleration properties -in the ultra relativistic flow regime of $\Gamma \sim
10-10^{3}$- such as angular distribution, acceleration time constant, particle
energy gain versus number of crossings and spectral shapes. We perform
calculations for sub-luminal and super-luminal shocks, using two different
approaches respectively. The $\Gamma^{2}$ energization for the first crossing
cycle and the significantly large energy gain for subsequent crossings as well
as the high 'speed up' factors found, are important in supporting the Vietri
and Waxman models on GRB ultra-high energy cosmic ray, neutrino, and gamma-ray
output.
