We examine the dynamics of electronic transitions into the shallow states of attractive impurity centers in GaAs through numerical simulations. The molecular dynamics based formulation circumvents the difficulty of having to evaluate "sticking functions," enables accurate computations of the phase-space distribution function, and allows microscopic treatment of both the carrier-phonon and carrier-carrier phenomena on an equal footing. Energy dependent trapping rates with and without the presence of external electric fields are obtained, and we consider situations involving both singly- and doubly-charged impurity centers. We show that initial trapping is reduced as a result of free-carrier screening, and hence detailed knowledge of both the trap density and the electronic concentration is necessary for a meaningful prediction of the trapping behavior. Finally, we also focus on modifications caused by electron-electron scattering, and find trapping enhancements due to the additional energy loss channel created by Auger-like phenomena.