Let f be a germ of an analytic function at infinity that can be analytically
continued along any path in the complex plane deprived of a finite set of
points, f \in\mathcal{A}(\bar{\C} \setminus A), \sharp A <\infty. J. Nuttall
has put forward the important relation between the maximal domain of f where
the function has a single-valued branch and the domain of convergence of the
diagonal Pade approximants for f. The Pade approximants, which are rational
functions and thus single-valued, approximate a holomorphic branch of f in the
domain of their convergence. At the same time most of their poles tend to the
boundary of the domain of convergence and the support of their limiting
distribution models the system of cuts that makes the function f single-valued.
Nuttall has conjectured (and proved for many important special cases) that this
system of cuts has minimal logarithmic capacity among all other systems
converting the function f to a single-valued branch. Thus the domain of
convergence corresponds to the maximal (in the sense of minimal boundary)
domain of single-valued holomorphy for the analytic function f
\in\mathcal{A}(\bar{\C} \setminus A). The complete proof of Nuttall's
conjecture (even in a more general setting where the set A has logarithmic
capacity zero) was obtained by H. Stahl. In this work, we derive strong
asymptotics for the denominators of the diagonal Pade approximants for this
problem in a rather general setting. We assume that A is a finite set of branch
points of f which have the algebraic character and which are placed in a
generic position. The last restriction means that we exclude from our
consideration some degenerated "constellations" of the branch points.Comment: 47 pages, 8 figure