Brownian dynamics simulations of trifunctional hyperbranched polymers (HP) of different molecular weight (N), degree of branching (DB), and Wiener index (W) have been performed under the influence of uniaxial elongational flow. Perfect trifuctional dendrimers with a trifunctional core up to the sixth generation were also studied for comparison. A freely jointed bead-rod model with excluded volume and hydrodynamic interactions has been used. The dependence of conformational properties and the intrinsic elongational viscosity on the flow rate were obtained. It was shown that both the degree of branching and the Wiener index significantly influence the conformational properties and the elongational viscosity of the molecules at all elongational rates. The coil-stretch transition was observed for all hyperbranched polymers with it being less pronounced than a linear polymer chain but more pronounced than a perfect dendrimer. Findings reveal that critical elongational rate scales as W-3. The dependence on N is weak and is not described by a power law. The orientation and the deformation of the HP is observed to occur in two stages as it was for a linear polymer and a dendrimer with a bifunctional core. The molecule first orients at low flow rate as a whole along the flow axis without significant deformation and local orientation. Increasing flow rate leads to local orientation on the level of the monomer and to significant global deformation of the molecule which plateaus at high flow. At high elongational flow rates, both the plateau value of the average squared radius of gyration and the plateau value of the elongational viscosity scale as approximately W. The dependence of these values on N is centered around N-0.48 and N-0.94 correspondingly. The ratio of /[eta(el)] does not change significantly but passes through a small and broad maximum during the transition.