A real-space implementation of the self-consistent field theory (SCFT) has been used to study the morphologies of ABCD 4-miktoarm star block copolymers. For the sake of numerical tractability, the morphologies and the phase diagrams of ABCD 4-miktoarm star block copolymers are investigated in two dimensions (2D) by varying the volume fractions of the blocks and the interaction parameters. Many interesting and complex morphologies occur and compared with ABCD linear block copolymers; ABCD 4-miktoarm star block copolymers have more regular disciplines. We found that systems with similar components have similar morphologies and at the weaker segregation, the minority components always cannot separate from the other blocks and they easily dissolve to form one phase with other block(s), but with the increase of the segregation degree (large (x) over bar), the ordered phases can be well separated. With the help of our computational prediction, experimental researchers can work more purposefully and efficiently. (c) 2007 Elsevier Ltd. All rights reserved.