Not sure if this helps or not but it explains the growth of the sunflower.

In September the fields and roadsides of the Great Plains erupt in a blaze of yellow as the sunflowers and goldenrods (also members of the sunflower family) make their presence known to the local pollinating insects. While many sunflower species may begin blooming in July, they are not as noticeable then as later on when they have grown up and over the surrounding vegetation. There are eleven species of sunflower recorded from Kansas. Most of them are perennials. Only the common sunflower and H. petiolaris, the Prairie Sunflower, are annuals. Identification of sunflowers can be very complicated because they frequently hybridize and even within species there is a high degree of variability. With a little practice, however, the most common species can be readily recognized.
Source(s):
http://www.gpnc.org/sunflower.htm

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Yes they do still keep growing after flowering
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