  We investigate the consequences of throwing point particles into
odd-dimensional Myers-Perry black holes in asymptotically anti-de Sitter (AdS)
backgrounds. We restrict our attention to the case in which the angular momenta
of the background geometry are all equal. This process allows us to test the
generalization of the weak cosmic censorship conjecture to asymptotically AdS
spacetimes in higher dimensions. We find no evidence for overspinning in D = 5,
7, 9 and 11 dimensions. Instead, test particles carrying the maximum possible
angular momentum that still fall into an extremal rotating black hole generate
a flow along the curve of extremal solutions.
