The concentration dependence of the relative viscosities of polybutadiene star polymers with 64, 128 and 270 arms has been investigated in the good solvent toluene. It is shown that the viscosity-concentration behavior of these stars matches that of hard-sphere suspensions. Near the overlap concentration c*, the star polymers form physical gels similar to the behavior of hard-spheres at the close packing volume fraction. Blending of two 128-arm stars with a large differences in size reduces the viscosity of the solutions and delays the gel formation to higher concentration. A sufficiently high segment density in the outer corona of the polymer coils is required in order to observe the hard-sphere viscosity-concentration profiles as demonstrated by the results on 32-arm stars and fuzzy 64-arm stars with 32-arms in the corona. In the case of a poly(butadiene-b-styrene) star a weak increase of the relative viscosity is observed at concentrations between two and three times the overlap concentration.