  Hadronic matrix elements of the vector, axial-vector and tensor currents
relevant for exclusive rare decays $B\to(\pi,\rho,K,K^*)\,l^+l^-$ induced by
the quark transition $b\to d,s$ are analysed using dispersion formulation of
the light-cone constituent quark model. The form factors in the decay region
are expressed as relativistic double spectral representations through the
light-cone wave functions of the initial and final mesons. These form factors
are shown to have the correct scaling properties in the limit of heavy-to-heavy
and heavy-to-light quark transitions in accordance with QCD. The dependence on
the quark-model parameters is studied.
