Coarse-grained molecular dynamics simulations are used to study the condensation of single polyanion chains with block copolymers composed of cationic and neutral blocks. The simulations are an effort to model complexes formed with DNA and cationic copolymers such as polyethylenimine-g-polyethylene glycol which have been used in gene delivery. The simulations reveal that increases in the cationic block length of the copolymer result in greater condensation of the polyanion. The ability of the complexes to form core-corona structures, with the neutral blocks of the copolymers forming a corona around a dense core formed from the charged beads, is investigated. The core-corona structure is shown to be dependent on both condensation of the polyanion chain and the length of the neutral block of the copolymer. Increasing the length of the cationic and neutral blocks of the copolymer both result in improvement in the core-corona structure. The internal structure of the complex core is shown to be a function of the architecture of the copolymer. Complexes formed from linear diblock copolymers have homogeneous cores with similarly arranged cationic and anionic beads; however, complexes formed with star-shaped copolymers have a layered core structure, with anionic beads found in the center of the cores.