The conformational behavior of both uncharged and charged hyperbranched polymers (HBPs) in dilute solutions has been studied using Brownian dynamics simulations. A distinction has been made between two types of architectures: type 1, which is characterized by its degree of polymerization (N) and its number of generations (gmax), and type 2, which is characterized by its degree of polymerization (N) and its degree of branching (DB). The radius of gyration (Rg) of both uncharged and charged type 1 HBPs is strongly influenced by variation of g. For uncharged type 2 HBPs Rg is relatively insensitive to variation of DB, whereas for charged type 2 HBPs Rg is a decreasing function of DB. The values of the radii of gyration as determined in the simulations are well reproduced in mean-field calculations. Scaling of Rg with the Wiener index and N has been investigated and compared to data from literature. The radial mass distribution of a charged type 1 HBP exhibits an ordering of the monomers that is highly dependent on g; the radial mass distribution of a charged type 2 HBPs shows an ordering that is only weakly dependent on DB. These orderings manifest themselves via oscillations of the static structure factor.