This is the largest stump that I photographed, but you can easily go larger with this technique. There is an upper limit on size, however. Keys are for scale. This stump was also drilled to let me apply a stump decomposition enhancer.
I'll bring the axe down a few times in one direction, then switch to about 90 degrees from the initial direction. Towards the end of the axe work, grab your handy spray bottle of herbicide and spray into the split wood. Don't over do it. Sometimes it helps to spray while the axe is still lodged in the stump since many splits tend to close up once the axe is removed. If you are resolute that you don't want to use herbicide, then don't - it's really a belt and suspenders approach. Splitting stumps exposes enough surface area that they tend to do very poorly in terms of resprouting, even without the herbicide.
- Posted at great expense from my iPhone