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We present results from a search for strong H2 absorption systems proximateto quasars (zabs~zem) in the Sloan Digital Sky Survey (SDSS) Data Release 14.The search is based on the Lyman-Werner band signature of damped H2 absorptionlines without any prior on the associated metal or neutral hydrogen content.This has resulted in the detection of 81 systems with log N(H2)~19-20 locatedwithin a few thousand km/s from the quasar. Compared to a control sample ofintervening systems, this implies an excess of proximate H2 systems by about afactor of 4 to 5. The incidence of H2 systems increases steeply with decreasingrelative velocity, reaching an order of magnitude higher than expected fromintervening statistics at Delta_v<1000 km/s. The most striking feature of theproximate systems compared to the intervening ones is the presence of Ly-alphaemission in the core of the associated damped HI absorption line in about halfof the sample. This puts constraints on the relative projected sizes of theabsorbing clouds to those of the quasar line emitting regions. Using the SDSSspectra, we estimate the HI, metal and dust content of the systems, which arefound to have typical metallicities of one tenth Solar, albeit with a largespread among individual systems. We observe trends between the fraction ofleaking Ly-alpha emission and the relative absorber-quasar velocity as well aswith the excitation of several metal species, similar to what has been seen inmetal-selected proximate DLAs. With the help of theoretical HI-H2 transitionrelations, we show that the presence of H2 helps to break the degeneracybetween density and strength of the UV field as main sources of excitation andhence provides unique constraints on the possible origin and location of theabsorbing clouds. We suggest that most of these systems originate from galaxiesin the quasar group. [truncated]

Proximate Molecular Quasar Absorbers: Excess of damped H2 systems at zabs~zQSO in SDSS DR14