The present invention provides a star polymer which comprises a central core and three or more branches bonded to the central core, and has a weight average molecular weight of from 1,000 to 100,000, wherein at least one of the branches containing at least one repeating unit selected from the group consisting of the following repeating units (1), (2), (3), (4) and (9); and a process for producing the star polymer. The present invention also provides a chemically amplified positive resist composition comprising the star polymer and an acid generator. ##STR00001##