  We present the results of a systematic Giant Metrewave Radio Telescope (GMRT)
survey of 21-cm absorption in a representative and unbiased sample of 35 strong
MgII systems in the redshift range: zabs~1.10-1.45, 33 of which have W_r>1 \AA.
The survey using ~400hrs of telescope time has resulted in 9 new 21-cm
detections and stringent 21-cm optical depth upper limits (median 3-sigma
optical depth per 10 km/s of 0.017) for the remaining 26 systems. This is by
far the largest number of 21-cm detections from any single survey of
intervening absorbers. Prior to our survey no intervening 21-cm system was
known in the above redshift range and only one system was known in the redshift
range 0.7<z<1.5. We discuss the relation between the detectability of 21-cm
absorption and various properties of UV absorption lines. We show that if MgII
systems are selected with the following criteria, MgII doublet ratio <1.3 and
W_r(MgI)/W_r(MgII)>0.3, then a detection rate of 21-cm absorption up to 90% can
be achieved. We estimate n_{21}, the number per unit redshift of 21-cm
absorbers with W_r(Mg(II)>W_o and integrated optical depth Tau_{21}>Tau_o and
show that n_{21} decreases with increasing redshift. In particular, for W_o=1.0
\AA and Tau_o>0.3 km\s, n_{21} falls by a factor 4 from <z>=0.5 to <z>=1.3. The
evolution seems to be stronger for stronger MgII systems. Using a subsample of
systems for which high frequency VLBA images are available, we show that the
effect is not related to the structure of the background radio sources and is
most probably due to the evolution of the cold neutral medium filling factor in
MgII systems. We find no correlation between the velocity spread of the 21-cm
absorption feature and W_r(MgII) at z~1.3.
