This paper describes the synthesis of three well defined, near monodisperse, heteroarm star block copolymers named as PI2(B13PS)(2), PI2(B26PS)(2), and PI2(B52PS)(2) where PI and PS refer to polyisoprene and polystyrene, respectively, and B refers to butadiene. The subscript in B indicates the number of butadiene units. The morphologies determined by transmission electron microscopy of these polymers are discussed. The theological properties were investigated and the results are compared with those of the related linear AB diblock and the hetero-4 arm star block copolymer PS2PI2 with simple architectures and no butadiene content. The polymer with the lowest number of butadiene units showed the highest T-ODT (200degreesC) while the polymer with the highest number showed the lowest T-ODT value (186degreesC). This is believed to be due, in part, to the ability of the PI arms to drag the small section of polybutadiene into their own territory causing the fluctuation of the interface from the connection point, and which also minimises the monomer correlation near the junction point. In addition, since the two PS anus of a star molecule are no longer constrained to occupy adjacent positions on the interface, the star begins to behave like a pair of PI-PS diblocks flexibly connected at their centres. Rheology also reveals the influence of a change of the linking on the linear viscoelastic properties. On increasing the amount of butadiene, a shoulder present in the time-temperature superposition (TTS) master curve of PS2PI2 having simple architecture is reduced in magnitude and almost disappears for the polymer having the highest number of butadiene units. (C) 2004 Elsevier Ltd. All rights reserved.