I missed a word "recursively", that I have edited in my original comment now.
replyConsider connected regions in the domain that have the same label. Much like countries on a political map. The situation where this has a short description in terms of recursive subdivision of space, is what I am calling a partitioned structure. It's really rather tautological.
"recursively partitioned" sounds like a fractal to me. Not sure what you really mean.
replyTaken to the limit you are absolutely right.
replyIt turns out many dataset have such a fractal like nature but where the partitioning needs to be cut off at a certain depth and not continued till infinity.