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We consider row sequences of (type II) Hermite-Padé approximations with common denominator associated with a vector f of formal power expansions about the origin. In terms of the asymptotic behavior of the sequence of common denominators, we describe some analytic properties of f and restate some conjectures corresponding to questions once posed by A. A. Gonchar for row sequences of Padé approximants. [ABSTRACT FROM AUTHOR]

Abstract: We prove the relative asymptotic behavior for the ratio of two sequences of multiple orthogonal polynomials with respect to the Nikishin systems of measures. The first Nikishin system is such that for each , has a constant sign on its compact support consisting of an interval , on which almost everywhere, and a discrete set without accumulation points in . If denotes the smallest interval containing , we assume that , . The second Nikishin system is a perturbation of the first by means of rational functions , , whose zeros and poles lie in . [Copyright &y& Elsevier]

Abstract: We prove ratio asymptotic for sequences of multiple orthogonal polynomials with respect to a Nikishin system of measures such that for each k, has constant sign on its support consisting on an interval , on which almost everywhere, and a set without accumulation points in . [Copyright &y& Elsevier]