  We present HIRES/Keck profiles of four extremely strong (W_r > 1.8 A) Mg II
absorbers at 1 < z < 2. The profiles display a common kinematic structure,
having a sharp drop in optical depth near the center of the profile and strong,
black-bottomed absorption on either side. This ``symmetric-inverted''
structure, with a velocity spread of several hundred kilometers per second, is
suggestive of superwinds arising in actively star-forming galaxies.
Low-ionization absorption of similar strength has been observed in local
star-forming galaxies.
  The Mg II absorbers with W_r > 1.8 A evolve away from z = 2 to the present.
We propose that a substantial fraction of these very strong absorbers are due
to superwinds and that their evolution is related to the redshift evolution of
star-forming galaxies. Based on the observed redshift number density of W_r >
1.8 A Mg II absorbers at 1 < z < 2, we explore whether it is realistic that
superwinds from starbursting galaxies could give rise to these absorbers.
Finally, we do an analysis of the superwind connection to damped Lya absorbers
(DLAs). DLAs and superwinds evolve differently and usually have different
kinematic structure, indicating that superwinds probably do not give rise to
the majority of DLAs.
