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