Anyway, thank you all for your help so far, and I'll be back for more.
As ugly as this plant (the paulownia) is, it's agressiveness is
utterly fascinating to me, moreso because I wonder how such an
aggressive tree could possibly be so uncommon????

In a word, it's *not* uncommon. princess tree is a nasty weed in places. If
you drive I40 from Asheville, NC to Knoxville, TN, right through a
magnificent gorge of the Pigeon River, princess tree is the dominant tree in
many areas. It doesn't do well in undisturbed places, but a little
disturbance and the seeds will germinate and then lots of princess trees.

The saplings of princess trees are notorious for having leaves arranged in
any fashion possible: alternate, opposite, whorled and anything else! Young
leaves can be entire or toothed, unlobed or lobed, little or big!

Nasty tree!

Scott Ranger