I have been growing hostas under a very large maple tree for about 15 years. I would have moved them all to a new area except I am stubborn and REALLY wanted them there. So I just dig them up about every 3 years (one by one as I have a few minutes), remove the roots that are entangled with the hosta roots, remove the surface maple roots from the hole area, and put the hosta back in the same spot. Of course I will have to do the same thing in another 3 years, but it's worth doing in my opinion! I do this for each hosta even if it isn't showing a problem...yet. I had the same problem under a cottonwood tree, but for those hostas I moved them to a new location, where I thought they would not only thrive, but look better. I don't grow any perennials in pots because of our cold winter temperatures. I did plant a seedling hosta in a hollow of a 3 ft. long chunk of a branch, and last fall I covered the whole branch with a foot of mulch. It will be interesting to see this spring if the hosta survives!