How are the edge of spot lights managed. Is there a decrease in luminescence or a scattering of the light at the edge?

Spotlights use sets of lenses to focus the light that is emitted. Depending on the focusing power of the lenses you can have more or less scattering as you get further from the center of the beam- imagine the mechanism in a flashlight where you can cast a broader, but softer light vs. a narrower, more focused light.

@Dan, if your question is about how to code the edge of the spotlight, it's just a linear or some other interpolation between a fully "on" beam and darkness.