The blackening on the exterior of your pan begins with the polymerization of oils, which sometimes spill over, but often times collect there as a result of being aerosolized while you are cooking. This happens whether or not use use a splash screen. To have any luck cleaning this, you have to get it right after cooking, and you have to work at it quite a bit with an abrasive cleaner. When it first appears, if you catch it before burning, it is usually brown. After a couple of uses (or high heat, long enough) it will blacken and be even more difficult to remove. Some folks like a shiny exterior and will work at this diligently after each use. Personally, I don't give the exterior of my pans much attention. For the stainless ones, the inside is shiny and clean, the exterior is black and not so pretty to look at. I don't find it impacts the functionality at all.