### Conformal measures and matings between Kleinian groups and quadratic polynomials

Following results of McMullen concerning rational maps, we show that the limit set of matings between a certain class of representations of C₂ ∗ C₃ and quadratic polynomials carries δ-conformal measures, and that if the correspondence is geometrically finite then the real number δ is equal to the Hausdorff dimension of the limit set. Moreover, when f is the limit of a pinching deformation ${{f}_{t}}_{0\le t<1}$ we give sufficient conditions for the dynamical convergence of ${f}_{t}$.