Its "fruit" looks like long strings of grapes, 4 or 5 inches long, 2 or 3 at each level, except they are less than half the size of actual grapes, they are hard, pointy at the unattached end, with a tiny bit of red-colored stuff at that end.
When they split open, they let out stuff that's lighter and finer than cotton, looks a bit like cotton, but they float. It looks even more like milkweed when it's floating along, except milkweed has a big seed. This has a really small one.
Any guess what this is?
Regardless, I realize now that this is the stuff that clogs the screens on my soffits. I have a roof fan that runs up to 12 hours a day on really hot days, and every 5 years or so, I have had to remove a layer that is something like felt, or what you take out of your dryer lint trap. Now that this tree is dead, I doubt I'll have to do that. There may be another such tree, but I think it is far away.