  Conformational properties of regular dendrimers and more general
hyperbranched polymer stars with Gaussian statistics for the spacer chains
between branching points are revisited numerically. We investigate the scaling
for asymptotically long chains especially for fractal dimensions $d_f = 3$
(marginally compact) and $d_f = 2.5$ (diffusion limited aggregation). Power-law
stars obtained by imposing the number of additional arms per generation are
compared to truly self-similar stars. We discuss effects of weak excluded
volume interactions and sketch the regime where the Gaussian approximation
should hold in dense solutions and melts for sufficiently large spacer chains.
