Controlling the topology of a polymer is essential in determining its physical properties and processing. Even after numerous studies, obtaining a diverse array of topologies, particularly within the framework of hyperbranched systems, remains challenging. Here, we propose a synthetic approach to obtain highly tunable hyperbranched polyglycidol (hb-PG) using a frustrated Lewis pair of pyridine or tributylamine along with tris(pentafluorophenyl)borane, B(C6F5)(3), that not only influences the preferred activated monomer mechanism through hydrogen bonding with the glycidol monomer, but also facilitates the formation of unique polymer topologies. Notably, the frustrated Lewis pair containing pyridine was found to yield a branched polymer carrying cyclic structures (branched cyclic polymers) with an increased degree of branching, whereas the more sterically hindered tributylamine yielded hb-PG without a cyclic structure; these results were confirmed by MALDI-ToF analyses. Based on the unique topologies of the PGs, significant correlations between the topology and the bulk and solution states were investigated using SEC, DSC, and H-1 NMR diffusion-ordered spectroscopy.