Thanks Bill. I think with Hawth's Tools it would be easy enough to create a regular grid of points, offset so they fall in the centre of each grid cell. I've often wondered how ArcGIS treats points that fall between cells, ie right on the border between two. By definition a point has no dimensions, so it can't be said to straddle either cell. But at the same time the raster surface covers the whole area, so I wonder how ArcGIS treats the no-mans-land in between cells. Perhaps they shift the point by an infinitely small amount so that it is then contained within a cell? Interesting thought...