Do you know what variety you have? Some rudbeckias grow very tall. I have herbstonne and it needs to be supported (something I need to do pronto). If it's goldsturm and is flopping, it is entirely possible that it's in richer soil than it needs.

I once grew this in a planter mounted on my fence. It made a nice mound in the pot and then spilled over for about 2 feet(I had no trellis). I did not find it to be a very prolific grower, but it was not in full sun. A tree 3 feet in diameter might be a bit much for it, but it would probably be quite full in a pot with a few twigs in it. You could probably 'train' it into a nice shape. I've done that with sweet peas.

I am glad I can help! Try to squish them, if you are fast enough. I used to have them on only one type of plant. But they became a big problem within the next few years.

It's some kind of leaf disease or fungus, I can't remember the exact name. They still bloom, but looks ugly up close. I've started to yank them from my gardens due to the same thing. I do a full cleanup in the fall of all BES, but it hasn't helped curb the disease...so out they go. Such a shame, too, since they offer such a nice end of summer color.