For a sphere-like object, I've unwrapped it using sphere projection. The resulting UV looks like this, with a single vertex at the pole (ignore the squiggly lines for now):
I would like to modify this to be more similar to blender's default mapping for a UV sphere, which separates the top vertex into multiple triangles with an even spread:
Is there a way to do this quickly and perfectly, that isn't just repeatedly ripping vertices and trying to eyeball their placement?
You can reproduce the results of the first image by viewing a UV sphere from the side and pressing U -> "Sphere projection" while in edit mode.