Copolymerization of ethylene and styrene with the catalytic system Cp*TiMe3-B(C6F5)(3) under suitable conditions affords a new polymer having a polyethylenic backbone with 4-phenyl-1-butyl branches as the main product. This unexpected result has been ascribed to the multi-site nature of the catalytic system, containing a species able to co-oligomerize ethylene and styrene to 6-phenyl-1-hexene (which was actually identified in the polymerization mixture), and another species able to copolymerize the latter with ethylene.