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In the first part of the present paper, we continue our study of the distribution of postcritically finite parameters in the moduli space of polynomials: we show the equidistribution of Misiurewicz and parabolic parameters with prescribed combinatorics toward the bifurcation measure. Our results essentially rely on a combinatorial description of the escape locus and of the bifurcation measure developped by Kiwi and Dujardin-Favre. In the second part of the paper, we construct a bifurcationdoi:10.4064/fm220-2-2018 fatcat:razwz62wcbhnziy6dsc3ppkt4q