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Transferring annotations of single-cell-, spatial- and multi-omics data is often challenging owing both to technical limitations, such as low spatial resolution or high dropout fraction, and to biological variations, such as continuous spectra of cell states. Based on the concept that these data are often best described as continuous mixtures of cells or molecules, we present a computational framework for the transfer of annotations to cells and their combinations (TACCO), which consists of an optimal transport model extended with different wrappers to annotate a wide variety of data. We apply TACCO to identify cell types and states, decipher spatiomolecular tissue structure at the cell and molecular level and resolve differentiation trajectories using synthetic and biological datasets. While matching or exceeding the accuracy of specialized tools for the individual tasks, TACCO reduces the computational requirements by up to an order of magnitude and scales to larger datasets (for example, considering the runtime of annotation transfer for 1 M simulated dropout observations).