  We calculate the form factors for weak decays of $B_{(s)}$ and $D_{(s)}$
mesons to light pseudoscalar and vector mesons within 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 effective
quark masses and meson wave functions are determined 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 $D\to (K,K^*)l\nu$ decay rates.
This allows us to predict numerous form factors for all kinematically
accessible $q^2$ values.
