Not sure if Vertex Extrude or Vertex Bevel is the right word, but I could really use this tool, is it in blender or does anyone know of a script that can do it for me.
Sorry if this was posted recently, I searched and found nothing.
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Use the bevel center script with a single vert selected. It replaces the 4 central triangles with a face though. Also since blender only has 3 and 4 sided faces you will get some extra edges. Best to quickly subdivide a plane, select a vert and bevel center and see what happens.
GreyBeard