  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.
