  Weak transition form factors among heavy pseudoscalar mesons are investigated
within a relativistic quark model formulated on the light-front. It is shown
that the light-front result derived in the time-like region for the matrix
elements of the plus component of the weak vector current coincides with the
spectator pole term of the quark triangle diagram. For the first time, the
dependence of the form factors on the squared four-momentum transfer $q^2$ is
calculated in the whole accessible kinematical region $0 \leq q^2 \leq
q^2_{max}$. For the numerical investigations of the semileptonic $B \to D \ell
\nu_{\ell}$, $B \to \pi \ell \nu_{\ell}$, $D \to K \ell \nu_{\ell}$ and $D \to
\pi \ell \nu_{\ell}$, the equal-time wave functions corresponding to the
updated version of the ISGW model are adopted. Our results for the form factors
and the decay rates are presented and compared with available experimental data
and predictions of different approaches. Moreover, the $K^0_L \to \pi^{\pm} ~
e^{\mp} ~ \nu_e$ decay is briefly discussed. Our approach is consistent with
experimental data.
