A process for preparing a radiation-curable, high-functionality, highly branched or hyperbranched polyurethane (meth)acrylate, comprising the reaction steps of (i) preparation of an adduct, that comprises one or more isocyanate groups and comprises at least one isocyanate-reactive group by reaction of a diisocyanate and/or a polyisocyanate with at least one compound having at least three isocyanate-reactive groups and/or at least one compound having two isocyanate-reactive groups, at least one of the components, (a) or (b), containing functional groups whose reactivity toward the functional groups of the other component is different, the more reactive groups from the compounds (a) and (b) being substantially consumed by reaction in step (i), and the reaction ratio being selected such that on average the adduct comprises at least one isocyanate-reactive group and one or more isocyanate groups, (ii)optionally, intermolecular addition reaction of the adduct from (i) to give a polyadduct, that comprises one or more isocyanate groups and may comprise at least one isocyanate-reactive group, (iii)optionally, reaction of the adduct from (i) or from (ii) with at least one monoiso-cyanate and/or with at least one diisocyanate or polyisocyanate or and/or with at least one diisocyanate or polyisocyanate which is different from the diisocyanate or polyisocyanate, and iv)reaction of the adduct from (i) and/or of the polyadduct from (ii) and/or of the reaction product from (iii) with at least one compound (c) which contains at least one, preferably precisely one, isocyanate-reactive group and at least one meth (acrylate) group, in which, in the course of the preparation, during reaction step (i) at least one polyether (meth) acrylate or a (meth) acrylate of a di-, tri- or tetraol is present which contains at least one radiation-curable group and which is inert toward the reactants from reaction step (i), the at least one polyether (meth) acrylate or (meth) acrylate of a di-, tri- or tetraol having an average molecular weight of up to 1000 g/mol. (i) preparation of an adduct, that comprises one or more isocyanate groups and comprises at least one isocyanate-reactive group by reaction of a diisocyanate and/or a polyisocyanate with at least one compound having at least three isocyanate-reactive groups and/or at least one compound having two isocyanate-reactive groups, at least one of the components, (a) or (b), containing functional groups whose reactivity toward the functional groups of the other component is different, the more reactive groups from the compounds (a) and (b) being substantially consumed by reaction in step (i), and the reaction ratio being selected such that on average the adduct comprises at least one isocyanate-reactive group and one or more isocyanate groups, a diisocyanate and/or a polyisocyanate at least one compound having at least three isocyanate-reactive groups and/or at least one compound having two isocyanate-reactive groups, (ii)optionally, intermolecular addition reaction of the adduct from (i) to give a polyadduct, that comprises one or more isocyanate groups and may comprise at least one isocyanate-reactive group, (iii)optionally, reaction of the adduct from (i) or from (ii) with at least one monoiso-cyanate and/or with at least one diisocyanate or polyisocyanate or and/or with at least one diisocyanate or polyisocyanate which is different from the diisocyanate or polyisocyanate, and iv)reaction of the adduct from (i) and/or of the polyadduct from (ii) and/or of the reaction product from (iii) with at least one compound (c) which contains at least one, preferably precisely one, isocyanate-reactive group and at least one meth (acrylate) group,