  Inspired by recent improved measurements of charm semileptonic decays at
BESIII, we study a large set of $D(D_s)$-meson semileptonic decays where the
hadron in the final state is one of $D^0$, $\rho$, $\omega$, $\eta^{(\prime)}$
in the case of $D^+$ decays, and $D^0$, $\phi$, $K^0$, $K^\ast(892)^0$,
$\eta^{(\prime)}$ in the case of $D^+_s$ decays. The required hadronic form
factors are computed in the full kinematical range of momentum transfer by
employing the covariant confined quark model developed by us. A detailed
comparison of the form factors with those from other approaches is provided. We
calculate the decay branching fractions and their ratios, which show good
agreement with available experimental data. We also give predictions for the
forward-backward asymmetry and the longitudinal and transverse polarizations of
the charged lepton in the final state.
