How can I propagate a Paulownia tree?
Something to consider before propagating this tree is its invasive potential. Depending on your location, increasing the population of Paulownia trees may not be wise. The U.S. Department of Agriculture lists Paulownia tomentosa as an invasive species. If you are in King County in Washington State, you may be interested to know that the Center for Invasive Species shows this tree in its Early Detection and Distribution map.
Nevertheless, directions for propagation are available. Peter Thompson’s book, Creative Propagation (2nd edition, Timber Press, 2005), states that Paulownia is best propagated by seed in the spring, or by semi-mature root cuttings laid horizontally just below the surface of the soil. I suggest that you think twice before propagating this tree.