Cutoff is an instance where a pixel/group of pixels besides an outline are directly next to a blank pixel/clashing pixel. This happens because the SNES cannot put two tiles at the same location in the same layer. It is not only very bad to look at but can cause undesirable results like Mario falling through the ground. That happens when a solid object is put over a non-solid one. It is highly frowned upon at Super Mario World Central, and most hacks with instances of cutoff are removed.
There are examples in the overworld too. When a hacker puts a 45 degree ledge, they must add a corner piece to it or else the darkened color at the edge of the ledge will clash with the bright color of the grass. This also applies in water, since it uses the same tileset.
Finally, sprite cutoff can occur if the sprite memory is at an improper setting. For example, if you have Banzai Bills in your level, but the sprite memory isn't set to 4, then Mario and some other sprites will disappear.
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