Ultrathin films of ZrO2 have been grown on r-cut sapphire [alpha-Al2O3(10<(12)over bar>)] substrates in the temperature range 50 degrees C)r-sapphire with [100]c-ZrO2 parallel to[12<(10)over bar>]r-sapphire. Above a critical thickness of 40 nm, monoclinic phase ZrO2 nucleates and coexists with the cubic ZrO2 phase. At faster growth rates (above 2 Angstrom/s), epitaxial single phase monoclinic ZrO2 is produced with the same epitaxial orientation as the cubic phase. For deposition below 250 degrees C, the ZrO2 films are amorphous. All of these films are stoichiometric ZrO2 as measured by x-ray photoelectron spectroscopy.