I feel as if I recall knowing how to do this, but alas time passes...
Anyway, what I'm trying to do is search a folder that contains many subfolders for a certain type of file (e.g., .gif) and then move all of those files to another drive but in the same folder structure (e.g., if the files are E:\Pics\Folder1\image1.gif and E:\Pics\Folder23\image7.gif and I want to move them to F:\Pics(overflow), then I'd wind up with F:\Pics(overflow)\Folder1\image1.gif and F:\Pics(overflow)\Folder23\image7.gif).