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We consider the relation of the multi-component 2D Toda hierarchy with matrixorthogonal and biorthogonal polynomials. The multi-graded Hankel reduction ofthis hierarchy is considered and the corresponding generalized matrixorthogonal polynomials are studied. In particular for these polynomials weconsider the recursion relations, and for rank one weights its relation withmultiple orthogonal polynomials of mixed type with a type II normalization andthe corresponding link with a Riemann--Hilbert problem.Comment: 15 page

The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann–Hilbert problems