Paulownia trees are planted as root cuttings while they are dormant. i.e in the winter time.
They need a fertile well drained spot, and need to be well watered and fed especially in their first year. They happily allow other species to grow succesfully as undergrowth as they make a deep tap root and drop nitrogen rich leaves each year..

Paulownia seedlings are available in New Zealand from productive trees new zealand.

Paulownia was traditionally planted at the birth of a daughter so that the much prized beautifully marked and light timber would be ready for making her dowry boxes and furniture as well as musical instruments when she married. . . Here at Olosurfer we planted ten trees in july 2007 to make into surfboards in the future.
Paulownia timber supplier in New Zealand
Here is a Paulownia tree sprouting in Spring time. . .
Six months later the trees are well over head: