The metastable orthorhombic phase of hafnia is generally obtained in polycrystalline films, whereas in epitaxial films, its formation has been much less investigated. We have grown Hf0.5Zr0.5O2 films by pulsed laser deposition, and the growth window (temperature and oxygen pressure during deposition and film thickness) for epitaxial stabilization of the ferroelectric phase is mapped. The remnant ferroelectric polarization, up to around 24 uC/cm2, depends on the amount of orthorhombic phase and interplanar spacing and increases with temperature and pressure for a fixed film thickness. The leakage current decreases with an increase in thickness or temperature, or when decreasing oxygen pressure. The coercive electric field (EC) depends on thickness (t) according to the coercive electric field (Ec) - thickness (t)-2/3 scaling, which is observed for the first time in ferroelectric hafnia, and the scaling extends to thicknesses down to around 5 nm. The proven ability to tailor the functional properties of high-quality epitaxial ferroelectric Hf0.5Zr0.5O2 films paves the way toward understanding their ferroelectric properties and prototyping devices.