The relationship between product structure and melt-state theological properties is established for series of branched PP derivatives prepared by the radical-mediated grafting of tri-functional coagents. Peroxide-initiated, solvent-free additions of linear PP to triallyl trimesate (TAM), trimethylol propane triacrylate (TMPTA) and triallyl phosphate (TAP) at high temperature are shown to produce bimodal molecular weight and branching distributions. Low-frequency dynamic shear viscosities as well as extensional viscosities are shown to be highly responsive to a hyper-branched chain population, whose abundance and molecular weight correlate with the kinetic chain length of the grafting process, and the propensity of a coagent to oligomerize. (C) 2008 Elsevier Ltd. All rights reserved.