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We give a new approach to the study of conformal iterated function systems with arbitrary overlaps. We provide lower and upper estimates for the Hausdorff dimension of the limit sets of such systems; these are expressed in terms of the topological pressure and the function d, counting overlaps. In the case when the function d is constant, we get an exact formula for the Hausdorff dimension. We also prove that in certain cases this formula holds if and only if the function d is constant.

Hausdorff dimension of the limit set of conformal iterated function systems with overlaps