Image 1 shows before editing. Image 2 shows 'edited line which i used too split with and with labels Close up in 3rd image.
I often split polygons with a line (ArcGIS 10.1 Split Polygon tool). In this case, and as an example: The polygons' boundary is coincident with a line (river); and opposite sides of the line/river. I re - digitise (to improve accuracy) the river and smooth the line. I then use this line to split the adjacent polygons. Often MANY small polygons (100+) are created and these are extremely cumbersome to manually integrate with the correct 'big polygon' they should be merged with. They are so small that it is by labeling them, they can be seen easily.
I usually seect them mannually and merge them with the correct polygon.