The recursive quantum mechanical string+3P0 model of polarized quark
fragmentation with pseudoscalar and vector meson production developed recently
has been implemented for the first time in a stand alone Monte Carlo program.
The program allows for a detailed study of the still unknown Collins effect for
vector meson production and of the effects of vector meson decays on the
Collins and dihadron asymmetries of the final observed hadrons.
In this talk we present the main results of the Monte Carlo simulations,
the comparison with the existing experimental data on SIDIS and e+e- annihilation to hadrons processes,
and predictions for possible new transverse spin asymmetries arising in the vector meson decay processes.
The theoretical aspects of the string+3P0 model are the subject of a different dedicated talk (X. Artru).