We fit the ultra high energy cosmic ray spectra above 10 ^ { 19 } \mathrm { 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 .