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w(\\lambda_j)d\\lambda_j,\\qquad \\theta\\geq 1. \\end{equation*} We prove that the biorthogonal polynomials associated to such models satisfy a recurrence relation and a Christoffel-Darboux formula if $\\theta\\in\\mathbb Q$, and that they can be characterized in terms of $1\\times 2$ vector-valued Riemann-Hilbert problems which exhibit some 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