What is acceptable tolerance for heat distribution in frying pan
You say the heat source doesn't matter, but it's probably the biggest effect.

Gas tends to give a hotter ring, possibly with a central burner giving a central hotspot on big burners.
Electric (resistive) depends on where it makes good contact - and both pan and ring probably aren't perfectly flat.
Induction should be quite even over the element (if the pan is good)
Halogen should again be fairly even over the element, though there's often a cooler spot in the middle.

In almost all cases a pan that overhangs will be cooler at the edges, which may or may not be a bad thing. Often a pan exactly the same size as an electric ring will be cooler at the edges, because more heat is lost there. On gas this may be reversed due to hot air rising up the sides.
The contents will tend to reduce the difference in temperature. This is obvious in boiling, where you've got convection and hotspots are limited by the water. In frying there's less to even it out, but moving the food around has the same effect when that's possible. Crepes (similarly omelettes), after distribution of the ingredients, of course don't get stirred, but still usually cook evenly.
I suspect in your case the ring is smaller than the pan; you may also find it gets more even with longer preheating. For some things, especially on gas, it can be good to preheat on maximum then allow the temperature to drop to what you want - part of the dropping is heat spreading out.