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I am trying to spatially join two tables containing polygons (let's call them table A and table B) so the ID of table A is joined to the table B only if the polygon centroids of table A are inside the polygons of table B.

Hope it makes sense?

I tried the spatial join, but the only option I could select is if the polygons of A are completely within the polygons B (second radio button) which is something I don't want.

4

You need to use spatial join from ArcToolbox, which has the option that you need "Have their centroid in" located under the Match Option, as you can see below:

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You can find the tool from ArcToolbox -> Analysis Tools -> Overlay -> Spatial Join

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