The critical behavior of black holes in even and odd dimensional space
times is studied based on Banados-Teitelboim-Zanelli dimensionally con
tinued black holes. In even dimensions it is found that asymptotically
hat and anti-de Sitter Reissner-Nordstrom black holes present up to t
wo second-order phase transitions. The case of asymptotically anti-de
Sitter-Schwarzschild black holes presents only one critical transition
and a minimum of temperature, which occurs at the transition. Finally
, it is shown that phase transitions are absent in odd dimensions.