How to link polygon features in one layer to polygon features in another, using large

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I have two polygon layers: the first one contains small land lots (green in the image), the second one contains large zones (the purple line in the image attached separates 2 such zones).

I want to link (the id's of) the large zones in layer 2 to the small parcels in layer one, using the largest overlap as criteria or measure: the small parcel gets the id of the large zone with which it has the largest overlap.

How can this be done in QGIS (also considering GRASS, SAGA...) or any other freeware GIS. ArcGIS (e.g. Overlay toolset) is not an option for me.

Thanks.





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