This work describes a one-pot synthesis of dendrite-like hyperbranched polyglycerols (HPGs) via a ring-opening multibranching polymerization (ROMBP) process using a bis(5,7-dichloro-2-methyl-8-quinolinolato)methyl aluminum complex () as a catalyst and 1,1,1-tris(hydroxymethyl)propane/trimethylol propane (TMP) as an initiator. Single-crystal X-ray diffraction (XRD) analysis was used to elucidate the molecular structure of complex . Inverse-gated (IG)C NMR analysis of HPGs showed degree of branching between 0.50 and 0.57. Gel permeation chromatography (GPC) analysis of the HPG polymers provided low, medium, and high-molecular weight ( ) polymers ranging from 14 to 73 kDa and molecular weight distributions ( / ) between 1.16 and 1.35. The obtained HPGs exhibited high wettability with water contact angle between 18 and 21° and ranging between -39 and -55 °C. Notably, ancillary ligand-supported aluminum complexes as catalysts for HPG polymerization reactions have not been reported to date. The obtained HPG polymers in the presence of the aluminum complex () can be used for various biomedical applications. Here, nanocomposite electrospun fibers were fabricated with synthesized HPG polymer. The nanofibers were subjected to cell culture experiments to evaluate cytocompatibility behavior with L929 and MG63 cells. The cytocompatibility studies of HPG polymer and nanocomposite scaffold showed high cell viability and spreading. The study results concluded, synthesized HPG polymers and composite nanofibers can be used for various biomedical applications.