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Using the vast statistics provided by both Euclid and the LOFAR surveys, we present the first large-scale study of the connection among radio emission, its morphology, and the merging properties of the hosts of radio sources up to z ∼ 2. By dividing the radio sample into active galactic nuclei (AGNs) and star-forming galaxies, we find that radio-emitting AGNs show a clear preference for residing within galaxies undergoing a merging event. This is more significant for AGNs that present complex or extended radio emission; indeed, about half of them are associated with merging systems, while only ∼15% are hosted by a non-interacting galaxy. The observed trend is primarily driven by AGNs residing at z < 1, especially in the case of high – P144 MHz > 1024 W Hz−1 sr−1 – radio luminosities (∼56% in mergers versus ∼10% in non-mergers regardless of radio appearance). On the other hand, this preference seems to disappear at higher redshifts, where only bright AGNs with extended radio emission still prefer galaxies undergoing a merging event. The situation is reversed in the case of radio-emitting star-forming galaxies, which are preferentially associated with non-interacting systems. This is more significant as we move towards low-radio-luminosity/star-formation objects (P144 MHz < 1023 W Hz−1 sr−1) for which we find ∼40% in non-mergers versus ∼20% in mergers. These values hold regardless of redshift. We interpreted the above result for AGNs with their need to accrete outer gas from local encounters in order to trigger (radio) activity, especially in the case of extended radio emission such as hot spots and lobes. This is mostly observed at z < 1, since galaxies in the local Universe are more gas deprived than their higher redshift counterparts. Internal gas reservoirs instead seem sufficient to trigger star formation within the majority of galaxies, which indeed mostly appear as non-interacting systems at all redshifts probed.