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In the image provided, I have drawn few polygons and a shapefile in red colour above them touching those polygons. Is there any way by which we could merge those polygons which, the red colour shapefile is touching.

At the end what I am expecting is that suppose the red polygon is touching 3 polygons, they should make it a single polygon(just the polygons which are touched by red polygon/shapefile)

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You can use Spatial Join for this operation. Make sure to select the JOIN_ONE_TO_MANY Join Operation as this will create a JOIN_FID field you can use to Dissolve the polygons. In sum, use the following workflow:

  1. Spatial Join with the "JOIN_ONE_TO_MANY" Join Operation and an "INTERSECT" match option
  2. Dissolve by "JOIN_FID" field
  • One to one you mean? – FelixIP Nov 28 '17 at 6:31
  • I believe in this case the join one to many operation is most appropriate. – Aaron Nov 28 '17 at 6:51

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