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The solubilising capacities of micelles of a linear-dendritic copolymer (BE-PAMAM), formed by conjugating the poly(butylene oxide) (B)–poly(ethylene oxide) (E) block copolymer B16E42 (BE) with a G2 PAMAM dendrimer, have been compared with those of the diblock copolymer B16E42 for the anti-cancer drug paclitaxel. The BE-PAMAM copolymer showed a greater solubility enhancement than BE under equivalent conditions. Drug-loading efficiency was improved using a solvent-loading method compared with the conventional solution-loading method. The solubility of paclitaxel was increased 3700-fold by micellar encapsulation in a 2% (w/v) BE–PAMAM copolymer solution at 37 °C using this solubilisation technique. Dynamic light scattering and transmission electron microscopy studies indicated a transition of spherical to worm-like micelles of the BE copolymer induced by the encapsulation of drug molecules. A sustained release of encapsulated drug was observed, with approximately 80% and 60% paclitaxel being released from 2% (w/v) solutions of BE and BE-PAMAM respectively after 24 h of dialysis at 37 °C.