  (Abridged) With the goal of investigating the nature of OVI absorbers at high
redshifts, we study the effects of proximity to the background quasar. In a
sample of sixteen quasars at z(QSO) between 2.14 and 2.87 observed at 6.6 km/s
resolution with VLT/UVES, we detect 35 OVI absorption-line systems lying within
8000 km/s of z(QSO). The systems can be categorized into 9 strong and 26 weak
OVI absorbers. The strong absorbers are defined by the presence of either
broad, fully saturated OVI absorption or partial coverage of the continuum
source, and have log N(OVI)>~15.0; these systems are intrinsic to the AGN. The
weak (narrow) systems show no partial coverage or saturation, and are
characterized by log N(OVI)<14.5 and have a median total velocity width of only
42 km/s. The incidence dN/dz of weak OVI systems within 2000 km/s of the quasar
is 42+/-12. Between 2000 and 8000 km/s, dN/dz falls to 14+/-4, equal to the
incidence of intervening OVI absorbers. Whereas the accompanying H I and C IV
column densities are significantly lower (by a mean of ~1 dex) in the weak OVI
absorbers within 2000 km/s of z(QSO) than in those at larger velocities, the
OVI column densities display no dependence on proximity. Furthermore,
significant offsets between the HI and OVI centroids in ~50% of the weak
absorbers imply that (at least in these cases) the HI and OVI are not formed in
the same phase of gas. In summary, we find no firm evidence that quasar
radiation influences the OVI-bearing gas, suggesting the OVI is collisionally
ionized rather than photoionized, possibly in the multi-phase halos of
foreground galaxies. Non-equilibrium collisional ionization models are needed
to explain the low temperatures in the absorbing gas, which are implied by
narrow line widths (b<14 km/s) in over half of the observed OVI components.
