Noncovalent nonspecific solubilization of carbon nanotubes with common polymers without having any specific functionality is an important strategy for rendering debundled nanotube solutions for their processing and technological applications. Among the various polymers investigated thus far for noncovalent nonspecific nanotube solubilization, hyperbranched polyethylene (HBPE) featured with distinct highly compact dendritic chain architecture has been discovered to show outstanding performance in rendering stable nanotube solutions in common low-polarity organic solvents (including tetrahydrofuran (THF) and chloroform) at surprisingly high concentrations. To understand the mechanism of the nanotube solubilization with this unique class of polymers and to elucidate the effects of various macromolecular structural parameters, we have designed and synthesized in this work four sets of highly branched polyethylenes varying in chain topology, molecular weight, and end group. With these polymers, we have systematically investigated and compared their performance for the solubilization of multi-walled carbon nanotubes in common solvents including THF, chloroform, n-heptane, and toluene. We have found that these macromolecular structural parameters as well as the solvent play complex but sensitive roles in this noncovalent solubilization system. This work thus provides some valuable guidelines towards the design of optimum polymers for efficient noncovalent nonspecific solubilization of carbon nanotubes.