Computer simulations on the self- and mutual-avoiding effects of two star polymers in a good solvent are reported where the number f of the branches has been extended to the region where no experimental results are yet available. A simple and efficient Monte Carlo (MC) sampling technique was used for the lattice-model simulations. Calculations were performed for 8-to 24-arm star polymers, which complement our previous work and also Rubio et al.'s off-lattice MC simulations. The radius of gyration, the total number of configurations, and its exponent gamma(f) are evaluated. The values of gamma(f) obtained are consistent with the large f behavior similar to f(3/2) predicted by Ohno (Phys. Rev. 1989, A40, 1424). The pair-distribution function, the second virial coefficient, and the penetration function are also evaluated. The first order epsilon-expansion, which is a naive approximation of the penetration function, has been known to become increasingly inaccurate for large f. The results of the simulations give further confirmation of the inaccuracy.