NOVELTY - A graft copolymer of a polyfarnesene with a condensation polymer, which is polyester, polycarbonate, polyamide, polyether, phenol-formaldehyde resin, urea-formaldehyde resin, and/or melamine-formaldehyde resin, is new.    USE - New graft copolymer of polyfarnesene with condensation polymer is used in polymer compositions used for films, sheets, foams, and molded products e.g. toys, grips, soft touch handles, bumper rub strips, floorings, auto floor mats, wheels, casters, furniture and appliance feet, tags, seals, gaskets, automotive doors, bumper fascia, grill components, rocker panels, hoses, linings, office supplies, seals, liners, diaphragms, tubes, lids, stoppers, plunger tips, delivery systems, kitchen wares, shoes, shoe bladders, and shoe soles (all claimed). Can also be used for hot-melt adhesives (used for freezer packaging of food products), pressure-sensitive adhesives, paper products, packaging materials, laminated wood panels, medical devices, disposal diapers, labels, hospital pads, sanitary napkins, surgical drapes, cartons, and bandages.    ADVANTAGE - The new graft copolymer of polyfarnesene with condensation polymer has unique physical, chemical and biological properties, and is environmentally-friendly or renewable.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) modified polyfarnesene prepared by reacting polyfarnesene with at least one modifier in the presence of a grafting initiator and/or radiation. The weight ratio of polyfarnesene and modifier is 100000:1-100:5. The modifier is cyclopentene-dione derivative of formula (I), butenal derivative of formula (II), acrylaldehyde derivative of formula (III), ethylene derivative of formula (IV), or tetrahydro-indene-dione derivative of formula (V); and    (2) polymer composition comprising the graft copolymer and additive(s).    Q1,Q6=O, S, NR23 or N-Q7;    Q2-Q5=halo, Q8, NR24R25, OR26 or O-Q8;    Q7,Q8=group of formula (i) or (ii);    k=1-10;    Q9=OH, NH2, NHR30, carboxy, epoxy or gycidyl;    R9-R30=H, or 1-20C alkyl, 1-20C alkenyl, 1-20C alkynyl, cycloalkyl, aryl, aralkyl, alkaryl, epoxy, or glycidyl (all optionally substituted), OH, NH2, or carboxy;    or R19+R22=optionally substituted -(CH2)m-;and    m=1-6.