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We study non-linearly the gravitational instabilities ofReissner-Nordstrom-de Sitter and Gauss-Bonnet-de Sitter black holes by usingthe large $D$ expansion method. In both cases, the thresholds of theinstability are found to be consistent with the linear analysis, and on thethresholds the evolutions of the black holes under perturbations settle down tostationary lumpy solutions. However, the solutions in unstable region arehighly time-dependent, and resemble the fully localized black spots and blackring with $S^{D-2}$ and $S^1\times S^{D-3}$ topologies, respectively. Our studyindicates the possible transition between the lumpy black holes and localizedblack holes in higher dimensions.

The Fate of Instability of de Sitter Black Holes at Large $D$