  We calculate the form factors for weak decays of $B_{(s)}$ and $D_{(s)}$
mesons to light pseudoscalar and vector mesons. To reveal the intimate
connection between different decay modes and to be able to perform the
calculations in the full physical $q^2$-region we use a relativistic dispersion
approach based on the constituent quark picture. This approach gives the form
factors as relativistic double spectral representations in terms of the wave
functions of the initial and final mesons. The form factors have the correct
analytic properties and satisfy general requirements of nonperturbative QCD in
the heavy quark limit.
  The disadvantages of quark models related to ill-defined effective quark
masses and not precisely known meson wave functions are reduced by fitting the
quark model parameters to lattice QCD results for the $B\to \rho$ transition
form factors at large momentum transfers and to the measured total $D\to
(K,K^*)l\nu$ decay rates. This allows us to predict numerous form factors for
all kinematically accessible $q^2$ values.
