Off-lattice Monte Carlo simulations were performed on linear and 12-ar
m star polymers in a good-solvent and in the Theta state to investigat
e both the molecular shape and the size distribution. We find that in
a good solvent the star polymer is more spherical than a random walk,
the more so the smaller its size is; moreover, a star of finite chain
length in the Theta state has a shape more similar to that in good sol
vent than to that in a random walk because of the excluded-volume rest
rictions that are particularly relevant in the core region. Both resul
ts are at variance with what is found in linear chains. Furthermore, t
he size distribution of the star is much narrower in a good solvent th
an in a random walk, approaching somewhat a delta function. This effec
t is also seen in the strong deformation of the density profile away f
rom the center of mass.