Structures in an electronic device such as substrates associated with a display may be bonded together using liquid adhesive. Fiber-based equipment may be used to apply ultraviolet light to peripheral edges of an adhesive layer during bonding. There-dimensional adhesive shapes may be produced using nozzles with adjustable openings, computer-controlled positioners, and other adhesive dispensing equipment. Ultraviolet light may be applied to liquid adhesive through a mask with an opacity gradient. Adjustable shutter structures may control adhesive exposure to ultraviolet light. Ultraviolet light exposure may be used to create an adhesive dam that helps create a well defined adhesive border. Multiple layers of adhesive may be applied between a pair of substrates.