This paper deals with the study of the accretion of dark energy with equation of state p = w \rho onto Kerr-Newman black holes .
We have obtained that when w > -1 the mass and specific angular momentum increase , and that whereas the specific angular momentum increases up to a given plateau , the mass grows up unboundedly .
On the regime where the dominant energy condition is violated our model predicts a steady decreasing of mass and angular momentum of black holes as phantom energy is being accreted .
Masses and angular momenta of all black holes tend to zero when one approaches the big rip .
The results that cosmic censorship is violated and that the black hole size increases beyond the universe size itself are discussed in terms of considering the used models as approximations to a more general descriptions where the metric is time-dependent .