  Let $ f_0 $ and $ f_\infty $ be formal power series at the origin and
infinity, and $ P_n/Q_n $, with $ \mathrm{deg}(P_n),\mathrm{deg}(Q_n)\leq n $,
be a rational function that simultaneously interpolates $ f_0 $ at the origin
with order $ n $ and $ f_\infty $ at infinity with order $ n+1 $. When germs $
f_0,f_\infty $ represent multi-valued functions with finitely many branch
points, it was shown by Buslaev that there exists a unique compact set $ F $ in
the complement of which the approximants converge in capacity to the
approximated functions. The set $ F $ might or might not separate the plane. We
study uniform convergence of the approximants for the geometrically simplest
sets $ F $ that do separate the plane.
