Hi Maryam
sounds like we're making progress. You can prevent the EucAlloc tool from spreading where it shouldn't by creating a background polygon that covers your analysis extent. One way to do that is to add a 'priority' field to your polygon feature class, create a rectangular background polygon, and give it a lower priority than the features you want to keep. For this to work, you'll also need to give your sliver polygons some id that you can use after rasterizing to turn the sliver cells into NODATA.
As an alternative, if you have the production mapping extension, you can create a 'difference polygon' in the editor, which will avoid creating any overlaps with the existing polygons.
For the raster to polygon step, did you specify 'SIMPLIFY' for the simplify option? Also, you can enable the 'create multipart features' option to do the dissolve as part of the conversion.
It may not be possible to remove all of the jaggies from this process. If you still have problems with the output, send me some anonymized input sample data and I'll see what I can do.
-jt