Can you provide me some hints on what algorithms might be used for dividing into smaller trees a Tree::Nary tree such as I have described?
No, since you don't describe why/how the trees should be split, but you would use unlink (Unlinks NODE from a tree, resulting in two separate trees. The NODE to unlink becomes the root of a new tree.).

You don't provide sample input/expected output, so read How do I post a question effectively? again please