The present invention relates to an assembly including: —a styling tool (5), in particular a straightening iron, to be moved along a lock of hair to which water and/or a cosmetic composition has been applied, and—a collecting device (7) coupled to the styling tool so as to collect a runoff generated during the movement of the tool over the hair on account of the presence of water and/or said composition on the hair, the collecting device having a reservoir (9) for picking up the runoff.