The invention relates to branched polysiloxane compositions resulting from copolymerizing under hydrosilylation conditions a component mixture comprising (a) one or more organosilicon compounds containing at least two unsaturated hydrocarbon functional groups per molecule, and (b) one or more silylhydride-containing compounds containing at least two silylhydride functional groups per molecule, with the provision that (i) at least one component (a) or (b) contains at least three functional groups per molecule; (ii) a component (a) or (b) having a higher number of functional groups per molecule is present in a molar amount equal to or lower than a molar amount of the other component (a) or (b) having a lower number of functional groups per molecule; and (iii) unsaturated hydrocarbon compounds are excluded from the component mixture.