Spliting small polygons and merge into the nearest-large polygons

[MaryamPanji]

Hello. I'm trying to split small polygons and merge them into the nearest _large polygons. With the Eliminate tool, the small polygons are merged into the large polygons but the boundaries between the two polygons look strange. Is there a way to do this automatically anyway? The feature class has thousands of small polygons that cannot be done manually.

After using Eliminate tool:

[MaryamPanji]

This picture showing how my issue with small polygons was solved. Just want to share with others if they have the same issue. 

[MaryamPanji]

Hi Jim,

Yes by enabling 'create multipart features' I don't have to use the dissolve tool. Thanks for that. 

Simplify has been ticked and I got those jaggies. About using background polygon, I'm a bit confused, cause I have polygons all over the country. 

Regarding the use of background polygons, I am a little confused because I have polygons around the country. I'm going to send you a part of the layer that has many geometry issues and the model builder I'm using for doing the whole process.