  We present large statistics simulations of 3-dimensional star polymers with
up to $f=80$ arms, and with up to 4000 monomers per arm for small values of
$f$. They were done for the Domb-Joyce model on the simple cubic lattice. This
is a model with soft core exclusion which allows multiple occupancy of sites
but punishes each same-site pair of monomers with a Boltzmann factor $v<1$. We
use this to allow all arms to be attached at the central site, and we use the
`magic' value $v=0.6$ to minimize corrections to scaling. The simulations are
made with a very efficient chain growth algorithm with resampling, PERM,
modified to allow simultaneous growth of all arms. This allows us to measure
not only the swelling (as observed from the center-to-end distances), but also
the partition sum. The latter gives very precise estimates of the critical
exponents $\gamma_f$. For completeness we made also extensive simulations of
linear (unbranched) polymers which give the best estimates for the exponent
$\gamma$.
