Black holes die hard: can one spin-up a black hole past extremality?

A possible process to destroy a black hole consists on throwing point particles with sufficiently large angular momentum into the black hole. In the case of Kerr black holes, it was shown by Wald that particles with dangerously large angular momentum are simply not captured by the hole, and thus the event horizon is not destroyed. Here we reconsider this gedanken experiment for a variety of black hole geometries, from black holes in higher dimensions to black rings. We show that this particular way of destroying a black hole does not succeed and that Cosmic Censorship is preserved.