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Using our sample of the most metal-rich damped Lyman $\alpha$ systems (DLAs)at z$\sim2$, and two literature compilations of chemical abundances in 341 DLAsand 2818 stars, we present an analysis of the chemical composition of DLAs inthe context of the Local Group. The metal-rich sample of DLAs at z$\sim2$probes metallicities as high as the Galactic disc and the most metal-rich dwarfspheroidals (dSphs), permitting an analysis of many elements typically observedin DLAs (Fe, Zn, Cr, Mn, Si, and S) in comparison to stellar abundancesobserved in the Galaxy and its satellites (in particular dSphs). Our mainconclusions are: (1) non-solar [Zn/Fe] abundances in metal-poor Galactic starsand in dSphs over the full metallicity range probed by DLAs, suggest that Zn isnot a simple proxy for Fe in DLAs and therefore not a suitable indicator ofdust depletion. After correcting for dust depletion, the majority of DLAs havesubsolar [Zn/Fe] similar to dSphs; (2) at [Fe/H]$\sim-0.5$, a constant[Mn/Fe]$\sim-0.5$ and near-solar [$\alpha$/Fe] (requiring an assumption aboutdust depletion) are in better agreement with dwarf galaxies than Galactic discstars; (3) [$\alpha$/Zn] is usually solar or subsolar in DLAs. However,although low ratios of [$\alpha$/Fe] are usually considered more `dwarf-like'than `Milky Way-like', subsolar [Zn/Fe] in Local Group dwarfs leads tosupersolar [$\alpha$/Zn] in the dSphs, in contrast with the DLAs. Therefore,whilst DLAs exhibit some similarities with the Local Group dwarf population,there are also notable differences.

The chemistry of the most metal-rich damped Lyman $\alpha$ systems at z$\sim2$ II. Context with the Local Group