  Given non-collinear points a_1, a_2, a_3, there is a unique compact, say
\Delta, that has minimal logarithmic capacity among all continua joining a_1,
a_2, and a_3. For h be a complex-valued non-vanishing Dini-continuous function
on \Delta, we consider f_h(z) := (1/\pi i)\int_\Delta h(t)/(t-z) dt/w^+(t),
where w(z) := \sqrt{\prod_{k=0}^3(z-a_k)} and w^+ the one-sided value according
to some orientation of \Delta. In this work we present strong asymptotics of
diagonal Pad\'e approximants to f_h and describe the behavior of the spurious
pole and the regions of locally uniform convergence from a generic perspective.
