  We find an exact solution in dimensionally continued gravity in arbitrary
dimensions which describes the gravitational collapse of a null dust fluid.
Considering the situation that a null dust fluid injects into the initially
anti-de Sitter spacetime, we show that a naked singularity can be formed. In
even dimensions, a massless ingoing null naked singularity emerges. In odd
dimensions, meanwhile, a massive timelike naked singularity forms. These naked
singularities can be globally naked if the ingoing null dust fluid is switched
off at a finite time; the resulting spacetime is static and asymptotically
anti-de Sitter spacetime. The curvature strength of the massive timelike naked
singularity in odd dimensions is independent of the spacetime dimensions or the
power of the mass function. This is a characteristic feature in Lovelock
gravity.
