I'm curious, of late, of which of Henry IV's sons would be most likely to be the progenitor of a successful cadet line that could rival either the main line or the house of York for influence. All three of the younger sons, the dukes of Clarence, Bedford, Gloucester, left illegitimate issue, so we know that the problem didn't lie with them. Obviously with the houses of York and Beaufort being further removed from the throne, a War of the Roses scenario (if it occurs) will more likely be between the descendants of Henry IV than the descendants of Edward III.