There is provided a composition for forming a hard coat layer which has high slippage and is excellent in water/oil repellency and also has antifouling properties such as fingerprint resistance and dirt wiping-off properties, and which is curable through ultraviolet irradiation in a nitrogen atmosphere or an air atmosphere that is generally used. A silicon-containing highly branched polymer obtained by polymerization of a monomer A having two or more radically polymerizable double bonds in a molecule and a monomer B having a polysiloxane chain and at least one radically polymerizable double bond in a molecule in the presence of a polymerization initiator D in an amount of 5 to 200% by mole relative to the number of moles of the monomer A; a curable composition comprising the highly branched polymer; a cured film obtained from the composition; and a hard coat film obtained by use of the composition.