TECHNOLOGY FOCUS - POLYMERS - Preferred Structure: The multi-branched polymer has structure of formula (II).Z=(CH2)z or p-phenylene group;z=0-3;R10-R13=aryl group having optional substituent, H, 1-6C alkyl, halogen atom or 1-6C alkoxyl group;t,u,v,w=0-3;X0,X1-X3=coupling group containing one atom of periodic table 14-16 groups;Y0,Y1-Y3=functional group of structure having an active halogen atom;p,q,r,s=integer more than 0 or 1;andQ0,Q1-Q3=arm portion having repeating unit derived by polymerizable unsaturated bond.Preferred Units: The repeating unit derived by polymerizable unsaturated bond is derived from at least one type of (meth)acrylic acid, (meth)acrylic-acid derivative, styrene, styrene derivative and vinyl group-containing heteroaryl compound. The repeating unit derived by polymerizable unsaturated bond, has repeating unit (a) derived from (meth)acrylic acid or (meth)acrylic-acid derivative, and repeating unit (c) derived from styrene or styrene derivative, in molar ratio of 95/5-70/30. The repeating unit (a) is of formula (a1) or repeating unit of formula (b1).R600=H or 1-6C alkyl;andE1=H, organic group having cycloaliphatic hydrocarbon structure or organic group having lactone ring.Preferred Property: The multi-branched polymer has weight average molecular weight of 10000-2000000. Preferred Definitions:    Ra=group of formula (Ia): -(-Xb-)-n2-R;    Xb=coupling group containing atom of periodic table (14-16) groups;    R=aryl group optionally having substituent, H, 1-6C alkyl, halogen atom or 1-6C alkoxyl group;and    n2=integer more than 0 or 1.    EXAMPLE - 1,1,2,2-tetrakis(4-hydroxyphenyl) ethane (in g) (20), triethylamine (25.3) and tetrahydrofuran (200 ml) were mixed in a flask. The solution was cooled at 0degreesC. Subsequently, 2-bromo isobutyryl bromide (50.58) diluted by tetrahydrofuran (50 ml), was added gradually, and cured at room temperature. The solvent was distilled from the filtrate. Subsequently, dichloromethane and water were added to the obtained residue, and organic layer was fractionated and dried by anhydrous magnesium sulfate. The obtained product was purified by silica gel column chromatography. The obtained crude product was recrystallized, and white crystal of multi-branched polymer (23.2) was obtained with 44% yield. The obtained polymer (0.25) and methyl methacrylate (10) were mixed with tetrahydrofuran (40). Dichloro tris (triphenyl phosphine) ruthenium (0.24) was added and mixed uniformly. Di-n-butylamine (0.13) was further added and heated at 60degreesC, and polymerization was started. The reaction mixture was polymerized for 7.5 hours, cooled at 0degreesC and polymerization was stopped. The reaction rate of methyl methacrylate was 54%. The reaction liquid was added to methanol, and crystal of polymer was filtered, dried under reduced pressure at 50degreesC for 5 hours, and light yellow crystal of multi-branched polymer (4.7) was obtained with 47% yield. The polymer was a mono-dispersed polymer with weight average molecular weight of 22000 and molecular weight distribution (ratio of weight average molecular weight to number average molecular weight) of 1.17.