Dip-coating, an important industrial technique, has been underexploited for preparing block copolymer (BC) thin films, such that the knowledge regarding their general characteristics is limited. Here, we present an overview of the crucial factors that determine how BC film morphology evolves as a function of dip-coating rate (withdrawal speed) over a wide range, illustrated using THF solutions of a polystyrene-b-poly(4-vinyl pyridine) (PS-P4VP) diblock copolymer mixed with two small molecules, naphthol and naphthoic acid, which are hydrogen-bonders with P4VP. Key factors in determining the film morphology are the systematic variation in film thickness and, for supramolecular BCs, in film composition with dip-coating rate. The former shows a general V-shaped dependence, related to the so-called capillarity and draining regimes identified previously for dip-coated sol-gel films. The relative small molecule content in the films studied is shown to increase in the capillarity regime from low to that of the dip-coating solution and thereafter to remain constant. Together, these changes, in addition to solvent and other effects, determine the film morphology and its evolution with dip-coating rate.