Functionalized ethylene alpha-olefin polymer additive useful in oleaginous compositions, said additive being prepared by contacting, simultaneously, (a) ethylene alpha-olefin starting polymer, (b) halogenating reactant, and (c) monounsaturated carboxylic acid producing reactant under reaction conditions effective to from a product mixture containing ethylene alpha-olefin polymer substituted with carboxylic moieties, said starting polymer (i) comprising monomer units derived from ethylene and at least one alpha-olefin of the formula H.sub.2 C.dbd.CHR.sup.1 wherein R.sup.1 is an alkyl group of from 1 to 18 carbon atoms, (ii) having a number average molecular weight of from about 700 to 15,000, (iii) having a molar ethylene content between about 20 to 80 percent, (iv) having an average of at least about 30% of polymer chains containing terminal ethenylidene unsaturation, and (v) having less than 5 wt. percent of a polymer fraction comprising polymer molecules having a molecular weight of less than about 300;
- and said functionalized polymer having a functionality of from about 0.5 to 2 and a VR value of less than about 4.1.