The "Italo-Hispano" rapier became widespread because the style of combat to which it was conducive became wide spread, although it must be noted that its heyday did not last to the 1800s, being almost entirely supplanted by the beginning of the 1700s with the shorter and more maneuverable small sword, and in turn the épée de combat and sabre, which would characterize most dueling of the late 19th-century. For a much longer treatment, I'd point you here, although I would point out that it is much more focused on the social forces that saw the rise of this style of combat, wherein:

[p]reviously duelists would hack away at each other for hours with cumbersome broadswords before either inflicting incapacitating wounds or ending the combat in mutual exhaustion [while] now a quick single thrust could prove fatal.

Than it is about discussing the rapier at great length.