Hi Ruth-Mary,
Off-hand flourishing is the term used to describe extensive flourishing that is done either with text or in the shape of something (as an ornate picture), usually a bird.
Off-hand referred to the method used (which involved a straight holder and throwing the strokes away from you) because the strokes were typically done in a continuous manner and not pre-planned (therefore "offhand"). However, I don't do it that way, I still use my oblique. And I draw most of it out before hand. At least the basic outline.
If I need correcting by someone who knows it better than I, please do!