  In 1986 J. Nuttall published in Constructive Approximation the paper
"Asymptotics of generalized Jacobi polynomials", where with his usual insight
he studied the behavior of the denominators ("generalized Jacobi polynomials")
and the remainders of the Pade approximants to a special class of algebraic
functions with 3 branch points. 25 years later we try to look at this problem
from a modern perspective. On one hand, the generalized Jacobi polynomials
constitute an instance of the so-called Heine-Stieltjes polynomials, i.e. they
are solutions of linear ODE with polynomial coefficients. On the other, they
satisfy complex orthogonality relations, and thus are suitable for the
Riemann-Hilbert asymptotic analysis. Along with the names mentioned in the
title, this paper features also a special appearance by Riemann surfaces,
quadratic differentials, compact sets of minimal capacity, special functions
and other characters.
