We present nebular emission associated with 198 strong Mg II absorbers at 0.35 $le z le$ 1.1 in the fibre spectra of quasars from the Sloan Digital Sky Survey. Measured [O II] luminosities (L$_{[O II]}$) are typical of sub-L$^{star}$ galaxies with derived star formation rate (uncorrected for fibre losses and dust reddening) in the range of 0.5-20 ${rm M_odot yr^{-1}}$. Typically less than $sim$ 3% of the Mg II systems with rest equivalent width, $W_{2796}$ $ge$ 2 AA, show L$_{[O II]} ge 0.3$ L$^{star}_{[O II]}$. The detection rate is found to increase with increasing $W_{2796}$ and $z$. No significant correlation is found between $W_{2796}$ and L$_{[O II]}$ even when we restrict the samples to narrow $z$-ranges. A strong correlation is seen between L$_{[O II]}$ and $z$. While this is expected from the luminosity evolution of galaxies, we show finite fibre size plays a very crucial role in this correlation. The measured nebular line ratios (like [O III]/[O II] and [O III]/H$beta$) and their $z$ evolution are consistent with those of galaxies detected in deep surveys. Based on the median stacked spectra, we infer the average metallicity (log Z $sim$8.3), ionization parameter (log $q$ $sim$7.5) and stellar mass (log (M/M$_odot$)$sim$9.3). The Mg II systems with nebular emission typically have $W_{2796}$ $ge 2$ AA, Mg II doublet ratio close to 1 and W(Fe II$lambda$2600)/$W_{2796}$ $sim 0.5$ as often seen in damped Ly$alpha$ and 21-cm absorbers at these redshifts. This is the biggest reported sample of [O II] emission from Mg II absorbers at low impact parameters ideally suited for probing various feedback processes at play in $zle 1$ galaxies.
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