A hyperbranched polymer includes a hyperbranched, hydrophobic molecular core, respective low molecular weight polyethyleneimine chains attached to at least three branches of the hyperbranched, hydrophobic molecular core, and respective polyethylene glycol chains attached to at least two other branches of the hyperbranched, hydrophobic molecular core. Examples of the hyperbranched polymer may be used to form hyperbranched polyplexes, and may be included in DNA or RNA delivery systems.