We calculate semileptonic form factors for the decays $B_c \to \eta_c \, l \nu$ and $B_c \to J/\psi \, l \nu$ over the entire $q^2$ range, using a highly improved lattice quark action for charm at several lattice spacings down to $a=0.045~$fm.
We have two ways of treating the $b$ quark: either with an $\cal O(\alpha_s)$ improved NRQCD formalism or by extrapolating a heavy mass $m_h$ to $m_b$ in the relativistic formalism.
Comparison of the two approaches provides an important cross-check of methodologies in lattice QCD.
Nonperturbative renormalisation of the currents in the relativistic theory also allows us then to fix NRQCD-charm normalisation for $b$ to $c$ decays such as $B \to D$ and $B \to D^*$.