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Context: The hierarchical model of galaxy formation suggests that galaxiesare continuously growing. However, our position inside the Milky Way preventsus from studying the disk edge. Truncations are low surface brightness featureslocated in the disk outskirts of external galaxies. They indicate where thedisk brightness abruptly drops and their location is thought to changedynamically. In previous analyses of Milky Way-like galaxies, truncations weredetected up to 3 kpc above the mid-plane but whether they remain present beyondthat height remains unclear.  Aims: Our goal is to determine whether truncations can be detected above 3kpc height in the Milky Way-like galaxy NGC 4565, thus establishing the actualdisk thickness. We also aim to study how the truncation relates to diskproperties such as star formation activity or the warp.  Methods: We perform a vertical study of the disk of NGC 4565 edge inunprecedented detail. We explore the truncation radius at different heightsabove/below the disk mid-plane (0<z<8 kpc) and at different wavelengths. We usenew ultra-deep optical data ($\mu_{g,\rm{lim}}=30.5$ mag arcsec$^{-2}$; $3\sigma$ within $10 \times 10$ arcsec$^{2}$ boxes) in the $g$, $r$ and $i$ broadbands, along with near- and far-ultraviolet, H$\alpha$, and \ion{H}{i}observations.  Results: We detect the truncation up to 4 kpc in the $g$, $r$ and $i$ultra-deep bands which is 1 kpc higher than in any previous study for anygalaxy. The radial position of the truncation remains constant up to 3 kpcwhile higher up it is located at a smaller radius. This result is independentof the wavelength but is affected by the presence of the warp.  Conclusions: We propose an inside-out growth scenario for the formation ofthe disk of NGC 4565. Our results point towards the truncation feature beinglinked to a star-forming threshold and to the onset of the disk warp.

The truncation of the disk of NGC 4565: Detected up to z=4 kpc, with star formation, and affected by the warp