Limitations associated with the use of linear biodegradable polyesters in the preparation of anticancer nano-based drug delivery systems (nanoDDS) have turned scientific attention to the utilization of branched-chain (co-)polymers. In this context, the present study evaluates the use of novel branched poly(ε-caprolactone) (PCL)-based copolymers of different architectures for the preparation of anticancer nanoparticle (NP)-based formulations, using paclitaxel (PTX) as a model drug. Specifically, three PCL-polyol branched polyesters, namely, a three-arm copolymer based on glycerol (PCL-GLY), a four-arm copolymer based on pentaerythritol (PCL-PE), and a five-arm copolymer based on xylitol (PCL-XYL), were synthesized via ring-opening polymerization and characterized by proton nuclear magnetic resonance (1H-NMR), gel permeation chromatography (GPC), intrinsic viscosity, differential scanning calorimetry (DSC), X-ray diffraction (XRD), and Fourier-transform infrared (FT-IR) spectroscopy and cytotoxicity. Then, PTX-loaded NPs were prepared by an oil-in-water emulsion. The size of the obtained NPs varied from 200 to 300 nm, while the drug was dispersed in crystalline form in all formulations. High encapsulation efficiency and high yields were obtained in all cases, while FTIR analysis showed no molecular drug polymer. Finally, in vitro drug release studies showed that the studied nanocarriers significantly enhanced the dissolution rate and extent of the drug.