(Abridged) We use VLT/UVES high-resolution optical spectroscopy of seven GRB afterglows at z_GRB>2 to investigate circumburst and interstellar plasma in the host galaxies. Our sample consists of GRBs 021004, 050730, 050820, 050922C, 060607, 071031, and 080310. Four of these spectra were taken in rapid-response mode, within 30 minutes of the Swift GRB detection. We identify several distinct categories of high-ion absorption at velocities close to z_GRB: (i) Strong high-ion components at z_GRB itself are always seen in OVI, CIV, and SiIV, and usually (in 6 of 7 cases) in NV. We discuss circumburst and interstellar models for the origin of this absorption. Using the non-detection of SIV* toward GRB 050730 together with a UV photo-excitation model, we place a lower limit of 400 pc on the distance of the SIV-bearing gas from the GRB. (ii) Complex, multi-component CIV and SiIV profiles extending over 100-400 km/s around z_GRB are observed in each spectrum; these velocity fields are similar to those measured in damped Lyman-alpha systems at similar redshifts, suggesting a galactic origin. (iii) Asymmetric, blueshifted, absorption-line wings covering 65-140 km/s are seen in the CIV, SiIV, and OVI profiles in 4 of the 7 spectra. The wing kinematics together with the observation that two wings show Galactic CIV/SiIV ratios suggest these features trace outflowing ISM gas in the GRB host galaxies. (iv) High-velocity (HV; 500-5000 km/s) components are detected in 6 of the 7 spectra. The HV components show diverse properties. In the cases of GRBs 071031 and 080310, both the ionization level (very high CIV/SiIV ratios and absence of neutral-phase absorption) and the kinematics of the HV components can be explained by Wolf-Rayet winds from the GRB progenitors.
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