Polymer architecture plays an important role in the solution, rheological, mechanical and processing behavior. In this series of two papers, we explore the role of branching, especially branch density, on the conformation and rheology of homopolymers. A series of model star-core hyperbranched polystyrenes (HBPS) with branch functionality, f, ranging from approximately 15 to 55, and branch molecular weight M-br of 5, 10, 20, and 50 kg/mol are synthesized and characterized via triple detection SEC3 for the molecular weight, polydispersity, intrinsic viscosity, and radius of gyration. Compared to linear polymers and symmetric stars with three and eight arms of the same total molecular weight, these polymers exhibit considerably lower radius of gyration, Mark-Houwink exponent, and intrinsic viscosity. The hydrodynamic radii of HBPS with the highest branch density (f approximate to 50) are only about half the corresponding values of linear polymers of the same molecular weight, whereas this ratio is equal to 0.8 for symmetric stars. Our measurements suggest that HBPS have a very compact shape, high segmental density, and a starlike architecture. HBPS with branches shorter than the characteristic critical molecular weight exhibit a linear dependence of zero-shear viscosity on molecular weight, suggesting a lack of entanglements, and further indicating the starlike nature of the HBPS. Study of the rheology and flow birefringence of model polystyrenes will be presented in the following publication in this journal.