Agree with saltcedar. In parts of the USA Paulownia tomentosa is concidered to be an invasive plant. See.... http://www.nps.gov/plants/alien/fact/pato1.htm
Perhaps not a problem there in Wichita. Did this one pop up on its own, or might it have been planted? Flowering and setting of seed must occur before weediness results. Even then the climate must be suitable. Here, where we have dry summers I have seen few seedlings - all of them in rock work, as though the stones were providing some protection from drying out (as is the case with cactus seedlings in the wild). The only patch of numerous seedlings I have seen was in the neighbor's heavily watered garden across the street, which probably was providing a facsimile of the rainy eastern North American summer climate where this species is a problem (and the similar conditions in its native eastern Asian homeland).
