  We present the form factors of the $B\to\pi,\rho$ transitions induced by the
$b\to u$ quark currents at all kinematically accessible $q^2$. Our analysis is
based on the spectral representations of the form factors within the
constituent quark picture: we fix the soft meson wave functions and the
constituent quark masses by fitting $A_1(q^2)$ and $T_2(q^2)$ to the lattice
results at small recoils ($17\lesssim q^2\lesssim 20 GeV^2$). We then calculate
the $B\to\pi,\rho$ transition form factors down to $q^2=0$. For the $B\to\pi$
case the region $q^2\lesssim 20 GeV^2$ however does not cover the whole
kinematically accessible range. Due to the smallness of the pion mass the
region of small recoils is close to the nearby $B^*(5234)$ resonance. We
develop a parametrization which includes the $B^*$ dominance of the form
factors $f_+$ and $f_-$ at small recoils and numerically reproduces the results
of calculations at $q^2\lesssim 20 GeV^2$. We find
$\Gamma(B\to\pi\ell\nu)=8.0^{+0.8}_{-0.2} |V_{ub}|^2 $ps$^{-1}$ and
$\Gamma(B\to\rho\ell\nu)=15.8\pm 2.3 |V_{ub}|^2 $ps$^{-1}$.
