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Библиогр.: 52 назв.

Having in mind extensions of 2D holography beyond the Jackiw-Teitelboim model we propose holographic counterterms and asymptotic conditions for a family of asymptotically AdS2 dilaton gravity models leading to a consistent variational problem and a finite on-shell action. We show the presence of asymptotic Virasoro symmetries in all these models. The Schwarzian action generates (a part) of the equations of motion governing the asymptotic degrees of freedom. We also analyse the applicability of various entropy formulae. By a dilaton-dependent conformal transformation our results are extended to an even larger class of models having exotic asymptotic behavior. We also analyse asymptotic symmetries for some other classes of dilaton gravities without, however, constructing holographic counterterms.