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We investigate the asymptotic behavior for type II Hermite-Pade approximationto two functions, where each function has two branch points and the pairs ofbranch points are separated. We give a classification of the cases such thatthe limiting counting measures for the poles of the Hermite-Pade approximantsare described by an algebraic function of order 3 and genus 0. This situationgives rise to a vector-potential equilibrium problem for three measures and thepoles of the common denominator are asymptotically distributed like one ofthese measures. We also work out the strong asymptotics for the correspondingHermite-Pade approximants by using a 3x3 Riemann-Hilbert problem thatcharacterizes this Hermite-Pade approximation problem.

Asymptotics for Hermite-Pade rational approximants for two analytic functions with separated pairs of branch points (case of genus 0)