  We present the analytic expressions for the color-planar contributions to the
heavy-light form factors at three loops in perturbative QCD. These form factors
play an important role in the precision predictions of various observables in
top quark and flavour physics. We compute the master integrals using the method
of differential equations. We perform the ultraviolet renormalization for all
the appearing fields and parameters. The analytic results for the renormalized
form factors are expressed in terms of generalized harmonic polylogarithms. We
also study the Sudakov behaviour of these form factors in the asymptotic limit,
which enables us to obtain the complete logarithmic three-loop and partial
four-loop contributions.
