How Best To Animate Growing Stems Of Some Flowers

I am designing an animated flash webpage, and would like some advice on the best way to animate the growing stalk of some 'flowers'. I have watched an online tutorial on drawing curved lines, and in this tutorial the line was drawn using a mask manually, i.e. the mask was transformed manually for each frame, which is OK for a few frames, but I would rather do this automatically if possible, as there will be 8 lines and quite a lot of frames. The trouble with say creating a motion tween for the mask layer is that this doesn't give enough control with curvy lines.

So I was wondering if there is another way, either in Flash CS4 or After Effects CS4. For instance, is there such a thing as a fill/stroke tween, which would fill a predefined line with a particular colour at a variable rate? Here is a rough draft of the kind of page I am wanting to design: So each of the stems would grow from the edges of the screen, then divide and continue to grow. The 'flowers' will grow and follow the end of the lines/stems as they grow larger.