Broussonetia papyrifera - paper mulberry
This fig and mulberry relative has a remarkable range of climate tolerance. Native to east Asia, it was carried by canoe throughout tropical Polynesia as a fiber crop for making tapa cloth. It has now naturalized extensively in many areas of the world, from Gainesville, Florida to Islamabad, Pakistan.
I came across some plants in full fruit at Arnold Arboretum September 2, 2010. This was my second chance to sample the fruit, last time was about 15 years ago. Since then I have become more accustomed to tropical fruits, but it still seems pretty weird to me! Imagine a hard ball with fleshy, juicy tentacles all around it. They taste very sweet (very little sour in the specimens at Arnold), and similar to figs. I stand by my previous description of "an inside-out fresh fig," but that sounds a little better to me now.
Probably not more than a novelty fruit or one to be popular with children, perhaps similar to Akebia or Decaisnea in that regard. Unless you want to get into making tapa cloth or other fiber-based uses which it is excellent for.
It suckers in Florida but not at Arnold, perhaps because they mow around it. Plants at Tripple Brook Farm sucker too. Male and female plants are seperate, perhaps if you are interested in it for fiber you might grow only male plants. Apparently it's wind-borne pollen is a major allergen. Pretty crazy-looking fruit though!