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The functional potential formalism is used to analyze stationary axisymmetricspaces in the Einstein-Maxwell-Dilaton theory. Performing a Legendretransformation, a ``Hamiltonian''is obtained, which allows to rewrite thedynamical equations in terms of three complex functions only. Using an ansatzresembling the one used by the harmonic maps ansatz, we express these threefunctions in terms of the harmonic parameters, studying the cases where theseparameters are real, and when they are complex. For each case, the set ofequations in terms of these harmonic parameters is derived, and several classesof solutions to the Einstein-Maxwell with arbitrary coupling constant to adilaton field are presented. Most of the known solutions of charged anddilatonic black holes are contained as special cases and can be non-triviallygeneralized in different ways.Comment: 26 pages of LaTeX, no figures. To appear in Classical and Quantum  Gravit

Class of Einstein-Maxwell dilatons, an ansatz for new families of rotating solutions