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This talk will present a comprehensive analysis of $\bar B_{(s)}^{(*)}\to D_{(s)}^{(*)}$ form factors within the heavy-quark expansion. Such form factors are key theoretical inputs for precision studies of semileptonic $b\to c\ell\nu$ transitions, with direct relevance for Standard-Model tests and for the determination of $|V_{cb}|$. The resulting analysis provide precise predictions for form factors and for phenomenologically relevant observables, including branching fractions, angular observables, and lepton-flavour-universality ratios. I will also discuss a new treatment of subthreshold branch cuts, which is important for a controlled estimate of truncation uncertainties at the percent level.