A general strategy for the preparation of well-defined diblock copolymers combining a random cascade-branched dendritic (i.e., hyperbranched) and a linear block has been developed. The strategy is based on a linear poly (styrene-b-butadiene) (PS-b-PB) diblock copolymer with high molecular weight PS block and short, functional 1,2-PB block, prepared by conventional anionic polymerization. The functional PB block is used for the grafting of branched AB(2)-type carbosilane monomers, resulting in the attachment of a hyperbranched structure to the backbone. Slow addition of the methyldi(undecenyl)silane monomers using Karstedt's catalyst permits control of the molecular weight of the hyperbranched block, resulting in high molecular weight linear-hyperbranched diblock copolymers. Molecular weights of the block copolymers ranged between 72 800 and 106 400 g/mol for M-n, and polydispersity (M) over bar (w)/(M) over bar (n) was low (typically below 1.1), as predicted by theory for slow monomer addition. Morphological studies by TEM, AFM, and SAXS on these systems demonstrate that various microdomain structures typical for microphase-separated block copolymers can be obtained upon increasing the size of the hyperbranched block with respect to the linear one, despite the strong architectural asymmetry of the linear-hyperbranched macromolecules. However, due to the hyperbranched structure and the crowding of the interface, an asymmetry of the phase diagram is observed. The linear-hyperbranched PS520-b-[PB47-hb-PCSi142] sample with 49 wt% of the hyperbranched component displayed the most unusual morphological behavior.