Brush-dampening systems are used in offset printing presses to deposit a fine layer of water on top of a lithographic plate. The interaction between a pick-up roll and a brush is an interesting and complex mechanical problem indicative of some devices that are, or may become, useful in novel mass transfer devices. A kinematic analysis is used to identify the contributions of three independent mechanisms: (1) a splitting action at the nip formed between the roller and the brush, (2) a wiping action identical to the movement of a brush on top of a solid surface, and (3) the absence of contact between roller and brush on some sectors of the roller. Existing related theories are modified to describe mechanisms (1) and (2). The resulting theory depends on two adjustable parameters inaccessible to experimental determination but with a very well defined physical meaning. Experimental results were performed in an actual printing unit. Agreement between experiments and theory provide a sound explanation to handle what would otherwise be a hopelessly complex physical problem.