  We fit the ultra high energy cosmic ray spectra above 10$^{19}$ eV with
different injection spectra at cosmic ray sources that are uniformly and
homogeneously distributed in the Universe. We conclude that the current UHE
spectra are consistent with power laws of index $\alpha$ between 2.4 and 2.7.
There is a slow dependence of these indices on the cosmological evolution of
the cosmic ray sources, which in this model determines the end of the galactic
cosmic rays spectrum.
