OK, so there wasn't a contest. But an anonymous commenter said, "Looks like cosmos," and from the images I found by way of Google, I do believe that's what my mystery plant is!
Thank you, Mysterious Person. This is why I allow anonymous comments.
The only thing that does not ring true is this, since mine are eight feet tall: "Cosmos give you a big bang for your buck. Growing carefree from seed, these annuals (meaning they grow just one year) fill a flowerbed with color and are great cut flowers. Cosmos grow anywhere from 1 foot to 3 feet high, depending on the variety."
Read more: How to Grow Cosmos | eHow.com http://www.ehow.com/how_6745_grow-cosmos.html#ixzz12of2WFoI