Hydrogen abstraction by growth precursors is the dominant process responsible for reducing the hydrogen content of amorphous silicon thin films grown from SiH(4) discharges at low temperatures. Besides direct (Eley-Rideal) abstraction, gas-phase radicals may first adsorb on the growth surface and abstract hydrogen in a subsequent process, giving rise to thermally activated precursor-mediated (PM) and Langmuir-Hinshelwood (LH) abstraction mechanisms. Using results of first-principles density functional theory (DFT) calculations on the interaction of SiH(3) radicals with the hydrogen-terminated Si(001)-(2x1) surface, we show that precursor-mediated abstraction mechanisms can be described by a chemisorbed SiH(3) radical hopping between overcoordinated surface Si atoms while being weakly bonded to the surface before encountering a favorable site for hydrogen abstraction. The calculated energy barrier of 0.39 eV for the PM abstraction reaction is commensurate with the calculated barrier of 0.43-0.47 eV for diffusion of SiH(3) on the hydrogen-terminated Si(001)-(2x1) surface, which allows the radical to sample the entire surface for hydrogen atoms to abstract. In addition, using the same type of DFT analysis we have found that LH reaction pathways involve bond breaking between the silicon atoms of the chemisorbed SiH(3) radical and the film prior to hydrogen abstraction. The LH reaction pathways exhibit energy barriers of 0.76 eV or higher, confining the abstraction only to nearest-neighbor hydrogens. Furthermore, we have found that LH processes compete with radical desorption from the hydrogen-terminated Si(001)-(2x1) surface and may be suppressed by the dissociation of chemisorbed SiH(3) radicals into lower surface hydrides. Analysis of molecular-dynamics simulations of the growth process of plasma deposited silicon films have revealed that qualitatively similar pathways for thermally activated hydrogen abstraction also occur commonly on the amorphous silicon growth surface.