In this work, we investigated the:effect of topological structures of block copolymers on the formation of the nanophase in epoxy thermosets containing amphiphilic block copolymers. Two block copolymers composed of poly(epsilon-caprolactone) (PCL) and poly(2,2,2-trifluoroethyl acrylate) (PTFEA) blocks were synthesized to possess linear, and star-shaped topologies. The star-shaped block copolymer composed a polyhedral oligomeric silsesquioxane (POSS) core and eight poly(e-caprolactone)-block-poly (2,2,2-trifluoroethyl acrylate) (PCL-b-PTFEA) diblock copolymer Both block copolymers were synthesized via the combination of ring-opening polymerization and reversible addition-fragmentation chain transfer/macro-Molecular design via the interchange of xanthate (RAFT/MADIX) proces; they were controlled to have identical compositions of copolymerization an lengths of blocks. Upon incorporating both block copolymers into epoxy thermosets, the spherical PTFEA nanophases, were,formed in all the cases. However, the sizes of PTFEA nanophases from the star-like block copolymer were significantly lower than those from the linear diblock copolymer. The difference in the nanostructures gave rise to the different glass transition behavior of the nanostructured thermosets. The dependence of PTFEA nanophases on the topologies of block copolymers is interpreted in terms of the conformation of the miscible subchain (viz. PCL) at the surface of PTFEA microdomains and the restriction of POSS cages on the demixing of the thermoset-philic block (viz. PCL).