In this contribution, we report full details of the ethylene, 1,3-butadiene, and propylene homopolymerization processes mediated by alkylated bis(trimethyl)silylamide lanthanide-grafted complexes using a density functional theory (DFT) study of the initiation and first propagation steps. These systems allows us (i) to examine the role of the grafting mode on the kinetics and thermodynamics of the three processes considered, (ii) to confirm the catalytic behavior of these grafted complexes in ethylene polymerization, (iii) to rationalize the experimental preference for 1,4-cis polymerization of 1,3-butadiene, and (iv) to provide unprecedented information on the catalytic activity of the lanthanide-grafted complex as a propylene hompolymerization catalyst.