Mudfoot, I agree this is very much like walking in its seamlessness.
Skidude72 and Epic are correct, in my view. It is usually better to look at a turn from middle to middle, or fall line to fall line in order to avoid the transitional pause that indicates, "I'm finished with this turn, now I'll ski across the hill to find a new place to start a new turn." This traverse to traverse approach is one of the big problems of ski teaching. Since the main motivation of students is to slow down, stop, and feel safe, we get sucked into stopping the motion in a completed turn. What they learn about that this first day is very hard to change. I really believe that one of the big differences between an intermediate and an expert skier is this mental configuration about transitions. It is a semantical difference that has enormous real life result.
Having said that, I think that staying in motion into the next turn is not the same as rushing the turn or banking. Those are different issues, that I would treat differently. "Move, but don't hurry." for example.
ssh's point is an interesting one--especially since he witnessed the penultimate trashing of my knee before I got a new one! Hilly's more visible movement in the transition, or the edge change, is powerful and directed enough so that he is really well aligned for the middle of the turn. This, by the way, is one of the strong points of his skiing in my view. When you do that well, you really can "work" the ski in the middle of the turn without appearing to do much work. It is clear to me that there is plenty of resilient tension in the legs to maintain what he wishes to maintain in terms of pressure, edge, and twist to carry himself across the hill. Many skiers, in a radius like this, DO go dead in the middle. This is the classic park and ride turn you describe, Steve. I don't think Hilly does that. I think he "drives" the turn throughout. But, yes, he's quieter towards the middle, because he can be.
Another way of looking at this I learned from my friend, aikido master, Tom Crum. He says, "Move like the river. Be still like the mountain." He explains that the mountain stillness is not rigid. It's a dynamic, living stillness full of power and potential. Some of my best skiing will occur when I carry this idea with me. It helps me bypass technical thought and just ski. I certainly see this aspect in Hilly, and in many other skiers whom I admire.
Thanks for your thoughts, guys.