  We study the semileptonic $b\to c$ decays of the lowest-lying triply-heavy
baryons made from $b$ and $c$ quarks in the limit $m_b, m_c \gg
\Lambda_\mathrm{QCD}$ and close to the zero recoil point. The separate heavy
quark spin symmetries strongly constrain the matrix elements, leading to single
form factors for $ccb\to ccc$, $bbc\to ccb$, and
  $bbb\to bbc$ baryon decays. We also study the effects on these systems of
using a $Y$-shaped confinement potential, as suggested by lattice QCD results
for the interaction between three static quarks.
