The electrical properties of ferroelectric Hf-Zr-O ultrathin films, particularly the dependences of remnant polarization, leakage current, coercive field, and breakdown field on the metal composition and film thickness, are systematically examined. Physical analyses show that the Hf-Zr-O films in this experiment consist of polycrystalline grains and contain both ferroelectric and dielectric phases. It is found that changes in metal composition and thickness strongly influence the remnant polarization and the leakage current simultaneously. In contrast, the coercive field was relatively unaffected by these parameters. This particular behavior of the coercive field suggests that the polarization switching in Hf-Zr-O films is predominantly determined by the nature of nanometer-scale ferroelectric domains dispersed in the films.