A transition metal catalyst component for polymerization, composed of a metal
complex
comprising specific ligands and a specific substituted boron group and having a
bridging group, which exhibits a very high activity for an olefin type (co)polymerization
or an olefin-aromatic vinyl compound copolymerization, whereby the molecular weight
of a copolymer obtainable, is high. A method for producing an olefin (co)polymer
and an aromatic vinyl compound-olefin copolymer, by means thereof.