Typically things were not as I had expected. I am now running results for a limited number of regions (203) carefully selected to give a range of sizes and to not be ambiguous. I am also looking at the error (distance from region centre) rather than dist to centroid (which I suppose would be spread independant of error).

Tommorrow is the day I am supposed to stop experimenting and start writing! I have some results, but I think I will need to keep at it whilst writing. The results are probably enough to know what the story is though.