  In analyzing maximally symmetric Lovelock black holes with non-planar horizon
topologies, many novel features have been observed. The existence of finite
radius singularities, a mass gap in the black hole spectrum and solutions
displaying multiple horizons are noteworthy examples. Naively, in all these
cases, the appearance of naked singularities seems unavoidable, leading to the
question of whether these theories are consistent gravity theories. We address
this question and show that whenever the cosmic censorship conjecture is
threaten, an instability generically shows up driving the system to a new
configuration with presumably no naked singularities. Also, the same kind of
instability shows up in the process of spherical black holes evaporation in
these theories, suggesting a new phase for their decay. We find circumstantial
evidence indicating that, contrary to many claims in the literature, the cosmic
censorship hypothesis holds in Lovelock theory.
