This paper reports a study on the dynamics of foil-based functional component self-alignment on big plastic substrates. We investigate the dependence of alignment time and final precision of stacking of foil dies on a number of system parameters, such as physical properties of assembly medium, size and weight of assembling dies and their initial misalignment. Using water as a medium for direct self-alignment, mm- and cm-sized square-shaped pre-marked foil dies were aligned with high accuracy (<30 µm) on patterned marked carriers. High-speed camera stage and image recognition tools were used for analyzing rapid capillary-driven self-alignment processes of marked foil dies. Experimental results were successfully benchmarked with analytical and numerical modeling. It is shown that there is a definite range of initial misalignment values allowing dies to align with high accuracy and yield within the same time window, whereas both under smaller and larger initial offsets, i.e. with dies correspondingly too close or too far from their target positions, yield and alignment precision is significantly lower. Our demonstration that mm- to cm-sized functional foils can be aligned with high accuracy opens the perspective of efficiently assembling interesting new systems such as separately manufactured sensors, paper batteries and RFIDs through this direct capillary-driven self-alignment approach.