BTW - just to follow up on this. I investigated the large block orders. They are all dark-pool fills. I'm unsure what to make of it. PS - I don't think it takes billions to push a large cap. Seems to me 10's of millions would be enough at the right times.
For example, BX @ 100K or more shares in one block trade through a dark pool. If that flips a few times, it's a significant % of adv.