  We study supersymmetric (extreme) domain walls in four-dimensional (4d) N=1
supergravity theories with a general dilaton coupling $\alpha > 0$. Type I
walls, which are static, planar (say, in ($x,y$) plane) configurations,
interpolate between Minkowski space-time and a vacuum with a varying dilaton
field. We classify their global space-time with respect to the value of the
coupling $\alpha$. $N=1$ supergravity with $\alpha =1$, an effective theory
from superstrings, provides a dividing line between the theories with
$\alpha>1$, where there is a naked (planar) singularity on one side of the
wall, and the theories with $\alpha<1$, where the singularity of the of the
wall is covered by the horizon. The global space-time (in $(t,z$) direction) of
the extreme walls with the coupling $\alpha$ is the same as the global
space-time (in ($t,r)$ direction) of the extreme magnetically charged black
holes with the coupling $1/\alpha$.
