  We study the $\bar\partial$ equation subject to various boundary value
conditions on bounded simply connected Lipschitz domains $D\subset\mathbb C$:
for the Dirichlet problem with datum in $L^p(bD, \sigma)$, this is simply a
restatement of the fact that members of the holomorphic Hardy spaces are
uniquely and completely determined by their boundary values. Here we identify
the maximal data spaces and obtain estimates in the maximal $p$-range for the
Dirichlet, Regularity-for-Dirichlet, Neumann, and Robin boundary conditions for
$\bar\partial$.
