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A map of 100° on a side extracted from Gaia DR2 and centered on Alpha Persei reveals two distinct structures - the Alpha Persei star cluster and a conspicuous stellar stream, as widely documented in recent literature. In this work we employ DBSCAN to assess individual stars' membership and attempt at separating stars belonging to the cluster and to the stream from the general field. In turn, we characterize the stream and investigate its relation with the cluster. The stream population turned out to be significantly older (5 ± 1 Gyr) than the cluster, and to be positioned ∼90 pc away from the cluster, in its background. The stream exhibits a sizeable thickness of ∼180 pc in the direction of the line of view. Finally, the stream harbors a prominent population of white dwarf stars. We estimated an upper limit of the stream mass of ∼6000M o˙. The stream would therefore be the leftover of a relatively massive old cluster. The surface density map of Alpha Persei indicates the presence of tidal tails. While it is tempting to ascribe their presence to the interaction with the disrupting old star cluster, we prefer to believe, conservatively, they are of Galactic origin. © 2020. The American Astronomical Society. All rights reserved..