  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 $z\le 1$ galaxies.

Astrophysics of Galaxies