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Two dimensional gravity with torsion is proved to be equivalent to specialtypes of generalized 2d dilaton gravity. E.g. in one version, the dilaton fieldis shown to be expressible by the extra scalar curvature, constructed for anindependent Lorentz connection corresponding to a nontrivial torsion.Elimination of that dilaton field yields an equivalent torsionless theory,nonpolynomial in curvature. These theories, although locally equivalent exhibitquite different global properties of the general solution. We discuss theexample of a (torsionless) dilaton theory equivalent to the $R^2 + T^2$--model.Each global solution of this model is shown to split into a set of globalsolutions of generalized dilaton gravity. In contrast to the theory withtorsion the equivalent dilaton one exhibits solutions which are asymptoticallyflat in special ranges of the parameters. In the simplest case of ordinarydilaton gravity we clarify the well known problem of removing the Schwarzschildsingularity by a field redefinition.Comment: 21 pages, 6 Postscript figure

Geometric interpretation and classification of global solutions in generalized dilaton gravity