Carolinazone, interesting comment you make about the rootstock of American types, I did not know that.
" If the rootstock is American it will eventually put out rootsuckers (sometimes at a fair distance from the tree). I don't think Asian rootstocks do that. Often the root suckers are mistaken for seedlings."
I have 3 adult asian persimmon trees, all over 30 yrs old in ground. I tried to cut down one of the trees since it was to close to a block wall (property border) but I did not have time so just used a chain saw to cut it down to 12" from ground level. That stump ended up having the rootstock growing up, and that tree has many of these root suckers you mention that came out 12" or more away from the stump (trunk) of the tree that is cut off. Now that rootstock branches are tall, over 8ft and it has never had any fruits yet. It will be interesting to see what type of fruit it has. I can see that the branches are much more vigorous and grow wild, maybe 6 ft per year or more. Much different from the rootstock that I have on the Matsumoto persimmon photos above which grows more like the named variety branches.