The paper is devoted to extremal problems of the geometric function theory of complex variable related with estimates of functionals defined on systems of non-overlapping domains. Till now, many such problems have not been solved, though some partial solutions are available. In the paper improved method is proposed for solving problems on extremal decomposition of the complex plane. The main results of the paper generalize and strengthening some known results in the theory of non-overlapping domains with free poles to the case of an arbitrary arrangement of systems of points on the complex plane.

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