The invention is directed to essentially saturated hydrocarbon polymer composition comprising essentially saturated hydrocarbon polymers having A) a backbone chain, B) a plurality of essentially hydrocarbyl sidechains connected to A), said sidechains each having a number-average molecular weight of from 2500 Daltons to 125,000 Daltons and a MWD by SEC of 1.0-3.5; and having A) a Newtonian limiting viscosity (&eegr;0) at 190° C. at least 50% greater than that of a linear olefinic polymer of the same chemical composition and weight average molecular weight, preferably at least twice as great as that of said linear polymer, B) a ratio of the rubbery plateau modulus at 190° C. to that of a linear polymer of the same chemical composition less than 0.5, preferably