Using small angle neutron scattering, we investigated the conformation of star polymers with functionalities ranging from f = 8 to f = 128 in a good solvent. The stars were made by anionic polymerization of isoprene or butadiene using multifunctional chlorosilane linking agents. Single star form factors at zero concentration were determined by extrapolating low concentration data to phi = 0. Conformations at finite concentrations were obtained by the zero average contrast method. In general the star form factors are well described in terms of the Daoud-Cotton scaling model. This concerns the molecular weight, functionality, and concentration dependence of R(G) as well as the shape of the form factor. In particular the step height between the low Q and asymptotic power law regime was found to follow an f3/2 law. Furthermore, with increasing functionality the star form factors were found to tend toward spherelike behavior, bearing evidence for a secondary maximum at the position of the third oscillation of the corresponding sphere form factor.