Start the split at and edge with the hatchet and place the wedge in the crack before removing the hatchet. I also find it handy to produce a couple of wedges first if splitting larger rounds.

This also makes it easier to remove the hatchet due to the decreased friction and not having sharp edges preventing you from rocking the hatchet back and forth. It can act as a wedge in the wood with less friction since only the center of the head should contact the wood up until the eye. I'm going to recommend a vintage North American hatchet with a high centerline.