A process for making a substantially saturated dendritic hydrocarbon polymer. The process has the following steps: (a) polymerizing an amount of one or more alkadiene monomers and/or one or more alkenylaromatic polymers under anionic conditions in the presence of a di- or tri-functional organic lithium initiator to produce a polyalkadiene defining a multiplicity of lithiated chain ends; (b) reacting the polyalkadiene with an amount of a tri- or di-functional silane coupling agent to form a dendritic polyalkadiene; and (c) hydrogenating the dendritic polyalkadiene to form a substantially saturated dendritic hydrocarbon polymer. Also a process for process for making a dendritic hydrocarbon polymer, comprising: (a) polymerizing an amount of one or more alkadiene monomers and/or one or more alkenylaromatic polymers under anionic conditions in the presence of a di- or tri-functional organic lithium initiator to produce a hydrocarbon polymer defining a multiplicity of lithiated chain ends; and (b) reacting the hydrocarbon polymer with an amount of a tri- or di-functional silane coupling agent to form a dendritic hydrocarbon polymer.