The present invention relates to a method to produce highly branched polymers with a polyolefin backbone structure of ethylene and precise control of the nature of the branching. In particular, the distribution of branch length and number of branches can be more precisely controlled via the polymerization method of the present invention. The method comprises using anionic chemistry to make unsaturated polydienes with a well-defined, highly-branched structure, and then hydrogenating these polydienes to form highly branched or dendritic saturated hydrocarbon polymers. Highly branched or dendritic polyethylene, ethylene-propylene copolymer and atactic polypropylene are among the saturated hydrocarbon polymers that can be anionically synthesized via the proper selection of diene monomer type, coupling agent, and hydrogenation conditions.