Learning-based methods to understand and model hand–object interactions (HOI) require a large amount of high-quality HOI data. One way to create HOI data is to transfer hand poses from a source object to another based on the objects' geometry. However, current methods for transferring hand poses between objects rely on shape matching, limiting the ability to transfer poses across different categories due to differences in their shapes and sizes. We observe that HOI often involves specific semantic parts of objects, which often have more consistent shapes across categories. Furthermore, constructing size-invariant correspondences between these parts is important for cross-category transfer. Based on these insights, we introduce a novel method, PartHOI, for part-based HOI transfer. Using a generalized cylinder representation to parameterize geometry of object parts, PartHOI establishes a robust geometric correspondence between object parts, and enables the transfer of contact points. Given the transferred points, we optimize a hand pose to fit the target object. Qualitative and quantitative results demonstrate that our method can generalize HOI transfers well even across categories of objects, and produce high-fidelity results that are superior to those of existing methods.