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We provide results for the full set of form factors describing semileptonic$B$-meson transitions to pseudoscalar mesons $\pi$, $K$, $\bar{D}$ and vectormesons $\rho$, $K^*$, $\bar{D}^*$. Our results are obtained within theframework of QCD Light-Cone Sum Rules with $B$-meson distribution amplitudes.We recalculate and confirm the results for the leading-twist two-particlecontributions in the literature. Furthermore, we calculate and provide newexpressions for the two-particle contributions up to twist four. Following newdevelopments for the three-particle distribution amplitudes, we calculate andprovide new results for the complete set of three-particle contributions up totwist four. The form factors are computed numerically at several phase spacepoints using up-to-date input parameters, including correlations across phasespace points and form factors. We use a model ansatz for all contributing$B$-meson distribution amplitudes that is self-consistent up to twist-fouraccuracy. We find that the higher-twist two-particle contributions have asubstantial impact on the results, and dominate over the three-particlecontributions. Our numerical results, including correlations, are provided asmachine-readable ancillary files. We discuss the qualitative phenomenologicalimpact of our results on the present $b$ anomalies.

$B\to P$ and $B\to V$ Form Factors from $B$-Meson Light-Cone Sum Rules beyond Leading Twist