Prewetting of surface densities. (A) (Left) Snapshot of a simulation where a polymer-dense droplet prewets the membrane surface even though droplets are unstable in the bulk. (Right) Time-averaged membrane, tether, and polymer compositions. (B) Schematic phase diagram in terms of membrane and bulk couplings. A single-phase system (black dot) can move into the surface coexistence region by increasing (purple arrow) or increasing (green arrow). The surface coexistence regime expands significantly near critical coupling, , and at larger . (C) Simulations at weak bulk and membrane coupling are brought into the coexistence region through increasing (purple) or (green). (D) Density of polymers as a function of distance from the membrane. A system at weak bulk and membrane couplings sees a single phase (purple; simulation in C, Lower Left) while systems at stronger membrane couplings see two coexisting polymer density profiles (blue; simulation in C, Lower Right).