In geometric function theory of a complex variable problems on extremal decomposition with free poles on the unit circle are well known. One of such problem is the problem on maximum of the functional $${r^\gamma }({B_0},0)\prod\limits_{k = 1}^n r ({B_k},{a_k}),$$ where B0, B1, B2,..., Bn, n ≥ 2, are pairwise disjoint domains in ¯𝔺, a0 = 0, |ak| = 1, $k = \overline {1,n}$ and γ ∈ 2 (0; n], r(B, a) is the inner radius of the domain, B ⊂ ¯𝔺, with respect to a point a ∈ B. In the paper we consider a more general problem in which restrictions on the geometry of the location of points ak, $k = \overline {1,n}$ are weakened.

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