(a) Schematic illustration of the system which contains a bulk contracting network that has some attractive interaction with the boundary. Experimentally, the interaction with the boundary can be enhanced by adding increasing concentrations of Bodipy-conjugated ActA that localizes to the water-oil interface and nucleates actin filaments there (Abu Shah and Keren, 2014). In simulations, we introduce a clutch that can engage and disengage stochastically, connecting the contracting actin network with the boundary (Appendix 2). The competition between the recentering force that drives the aggregate to the center and the attractive interaction with the boundary, leads to size-dependent localization. (b) The aggregate displacement as a function of droplet radius is shown for standard conditions (left), and samples supplemented with 25 nM (center) or 100 nM (right) Bodipy-ActA. The colored regions depict the different size ranges: small droplets that are primarily polar (red), intermediate range with both polar and symmetric droplets (yellow), and large droplets which are mostly centered (green). The dashed black line marks the droplet radius, and the dashed red line marks the displacement where the aggregate reaches the boundary (droplet radius minus aggregate radius). As the interaction with the boundary is enhanced by increasing ActA concentrations, larger droplets are found in a polar state. (c) Simulation results for the aggregate displacement as a function of droplet radius. The interaction with the boundary is enhanced by increasing the clutch engagement rate (kon) and decreasing the disengagement rate (koff), resulting in changes in the size-dependent localization of the aggregates that resemble the changes observed experimentally in (b).