A process for making a substantially saturated dendritic hydrocarbon polymer. The process has the following steps: (a) polymerizing an amount of a first alkadiene monomer under anionic conditions in the presence of a first organic monolithium initiator to produce a linear polyalkadiene having a lithiated chain end; (b) reacting the linear polyalkadiene with an amount of a second organic monolithium initiator in the presence of tetramethylethylene diamine to form a multilithiated polyalkadiene; (c) reacting the multilithiated polyalkadiene with an amount of a second alkadiene monomer to form a branched polyalkadiene; (d) repeating steps (b) and (c) with the branched polyalkadiene one or more times to prepare a dendritic polyalkadiene; and (e) hydrogenating the dendritic polyalkadiene to form the substantially saturated dendritic hydrocarbon polymer.