TECHNOLOGY FOCUS - POLYMERS - Preferred Polymers - The polymeric chain (A1) comprises:(1) a copolymer having a repeating unit (I) and a repeating unit (II);(2) a copolymer having a repeating unit (I) and a repeating unit (III), or a copolymer having a repeating unit (I), a repeating unit (II), and a repeating unit (III).R5 = H or methyl;R6, R7 = H or 1-6C alkyl;R8 = -CH=CH2, -C(CH3)=CH2 or -CO2R' (wherein R' is 1-6C alkyl);r = 0, 1 or 2The arm moiety comprises the polymeric chain (A1) and a polymeric chain (A2) having a repeating unit (A21) of (IV).R9 = H or methyl;R10 = H, 1-12C alkyl, an optionally substituted alicyclic hydrocarbyl group having 3 or more carbon atoms, an optionally substituted phenyl, or hetero cyclic group.The polymeric chain (A2) has a repeating unit (A21) and a repeating unit (A22) of (V).R11 = H, methyl or optionally substituted aryl;R12 = 1-6C alkyl or OR13 (R13 is H, 1-6C alkyl or a leaving group;t = 0,1,2 or 3.The arm moiety has a polymeric chain having a number average molecular weight of 1,000 - 100,000. The central nucleus is crosslinked with a polyfunctional coupling agent, which has two or more polymerisable double bond in one molecule and preferably represented by (VI).R14 = H or methyl;Y = O, S, r1r2N (here, r1 and r2 are hydrogen atom, 1-6C alkyl, or alkoxycarbonyl), optionally substituted methylene, optionally substituted phenylene and the like.A preferred star polymer has a number average molecular weight of 20,000 - 500,000 and the ratio of weight average molecular weight (Mw) and the number average molecular weight (Mn) (Mw/Mn) of 1.00 - 1.50. EXAMPLE - Synthesis of a star polymer having poly(p-hydroxystyrene-b-styrene) as an arm 450 g of toluene and 50 g of tetrahydrofurane were mixed and 9.8 mmol of n-butyl lithium was added and kept at -60 degreesC and 0.1 mol of p-t-butoxystyrene was added dropwise over 15 minutes then the reaction was further continued for 30 minutes and 0.35 mol of styrene was added thereto dropwise over 15 minutes and the reaction was continued for 90 minutes to give a polymer. The polymer was of monodisperse and had Mn of 10,300. The reaction system was heated to -40 degreesC and 32.4 mmol of divinyl benzene was added and reacted for 4 hours. The reactant was added in a large amount of methanol to give a star polymer having Mn of 72,000 (white powder). Grafting polyethylene oxide to the arm 10 g of the produced star polymer was dissolved in 200 g of THF and 16 mmol of t-butoxypotassium was added and stirred at 25 degreesC for 1 hour. The 4.2 g of ethylene oxide was added and reacted at 65 degreesC for 24 hours then acetic acid was added to stop the reaction and the reactant was added to a large amount of n-hexane to precipitate a polymer which was filtered out, washed and dried at 60 degreesC for 5 hours to give 14.2 g of a star polymer (white powder) wherein polyethylene oxide (Mn of 245) was grafted to the p-hydroxy styrene unit in the arm.