In this study, we present detailed theoretical and experimental investigations on full-area alloying from screen printed aluminum pastes on silicon surfaces for solar cell applications. We introduce a simple analytical model for the description of the alloying process derived from existing models for evaporated Al layers, which we adapt to printed Al pastes. Thereby, we particularly account for the recrystallization of Si within the paste particles, which we refer to as parasitic Si recrystallization. Applying our model, we demonstrate good accordance of calculated with measured eutectic layer thicknesses. We show that the model can be versatilely used to investigate screen-printed Al-alloyed contacts in detail: We demonstrate that the latent heat of the Al paste significantly influences the alloying process. Thus, the effective peak temperature of the alloying process can be several 100 degrees C below the set peak temperature of the firing furnace. By combining calculations of the effective peak temperature with measurements of the Al doping concentration, we determine a parameterization of the solid solubility of Al in Si down to the eutectic temperature of 577 degrees C. Our investigations therefore provide improved understanding of alloying from printed Al pastes and enable the specific optimization of Al-alloyed contacts.