Critical Behavior of Dimensionally Continued Black Holes

The critical behavior of black holes in even and odd dimensional spacetimes is studied based on Ba~nados-Teitelboim-Zanelli (BTZ) dimensionally continued black holes. In even dimensions it is found that asymptotically flat and anti de-Sitter Reissner-Nordstr"om black holes present up to two second order phase transitions. The case of asymptotically anti-de-Sitter Schwarzschild black holes present 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.