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To study chemical composition of metal-rich absorbers at high redshifts in order to understand their nature and to determine sources of their metal enrichment. From six spectra of high-z QSOs, we select eleven metal-rich, Z>Z_☉, and optically-thin to the ionizing radiation, N(HI)<10¹⁷cm^–2, absorption systems ranging between z=1.5 and z=2.9 and revealing lines of different ions in subsequent ionization stages. Computations are performed using the Monte Carlo inversion (MCI) procedure complemented with the adjustment of the spectral shape of the ionizing radiation. This procedure along with selection criteria for the absorption systems guarantee the accuracy of the ionization corrections and of the derived element abundances (C, N, O, Mg, Al, Si, Fe). The majority of the systems (10 from 11) show abundance patterns which relate them to outflows from low and intermediate mass stars. One absorber is enriched prevalently by SNe II, however, a low percentage of such systems in our sample is conditioned by the selection criteria. All systems have sub-kpc linear sizes along the line-of-sight with many less than ∼20pc. In several systems, silicon is deficient, presumably due to the depletion onto dust grains in the envelopes of dust-forming stars and the subsequent gas-dust separation. At any value of [C/H], nitrogen can be either deficient, [N/C]<0, or enhanced, [N/C]>0, which supposes that the nitrogen enrichment occurs irregularly. In some cases, the lines of MgII λλ2796, 2803 appear to be shifted, probably as a result of an enhanced content of heavy isotopes ²⁵Mg and ²⁶Mg in the absorbing gas relative to the solar isotopic composition. Seven absorbers are characterized by low mean ionization parameter U, logU←2.3, among them only one system has a redshift z>2 (z_abs=2.5745) whereas all others are found at z∼1.8. This statistics is not affected by any selection criteria and reflects the real rise in number of such systems at z<2.0. Comparing the space number density of metal-rich absorbers with the comoving density of star-forming galaxies at z∼2, we estimate that the circumgalactic volume of each galaxy is populated by ∼10⁷-10⁸ such absorbers with total mass ≲1/100th of the stellar galactic mass. Possible effects of high metal content on the peak values of star-forming and AGN activities at z∼2 are discussed.