  We investigate the spacetime of a thick gravitating domain wall for a general
potential $V(\Phi)$. Using general analytical arguments we show that all
nontrivial solutions fall into two categories: those interpretable as an
isolated domain wall with a cosmological event horizon, and those which are
pure false vacuum de Sitter solutions. Although this latter solution is always
unstable to the field rolling coherently to its true vacuum, we show that there
is an additional instability to wall formation if the scalar field does not
couple too strongly to gravity. Using the $\lambda \Phi^4$ and sine-Gordon
models as illustrative examples, we investigate the phase space of the
gravitating domain wall in detail numerically, following the solutions from
weak to strong gravity. We find excellent agreement with the analytic work.
Then, we analyse the domain wall in the presence of a cosmological constant
finding again the two kinds of solutions, wall and de Sitter, even in the
presence of a negative cosmological constant.
