The planar elongational melt rheology and structural properties of dendrimers and hyperbranched polymers of different molecular weights (generations 1-4) and their linear counterparts have been studied using nonequilibrium molecular dynamics simulation techniques in the isothermal-isobaric ensemble. The extensional viscosity showed three distinctive regions against strain-rate, including an initial Newtonian region at low strain-rates, followed by a thickening behavior at medium strain-rates and terminated with a thinning region at very high strain-rates, in agreement with the Sarkar and Gupta model [J. Rein. Plast. Comp. 20, 1473-1484 (2001)]. In addition, a structural analysis was performed to study the size, shape, and spatial distributions within globular dendrimers and hyperbranched polymer molecules under planar elongational flow (PEF). Ratios of the eigenvalues of the gyration tensor showed that contrary to shear flow, under PEF even at low strain rates, dendrimers and hyperbranched molecules have ellipsoidal conformations and change to a much more flattened prolate shape at higher strain rates. In combination with the eigenvalue ratios, the distribution of monomers from the central core of the molecules showed that the thickening region occurs due to branches being stretched, and terminal thinning behavior stems primarily from flow-induced alignment and finite extensibility effects. (C) 2014 The Society of Rheology.