Structures such as layers of material associated with an electronic device may be assembled using adhesive. The adhesive may be dispensed onto the surface of an electronic device layer in liquid form. The liquid adhesive material may be a liquid pressure sensitive adhesive precursor material. Patterned structures such as touch sensor electrodes, black ink masking layers, and other structures may be formed on the electronic device layer. The use of liquid adhesive material may help the adhesive material flow over the edges of the patterned structures without forming bubbles or voids. Following application of the liquid pressure sensitive adhesive precursor material, the liquid pressure sensitive adhesive precursor material may be cured to form a solid layer of pressure sensitive adhesive. The layer of material on which the solid layer of pressure sensitive adhesive has been formed may then be vacuum laminated to an additional electronic device layer.