  The space $S_\kappa$ is the Stone space of the $\kappa$-saturated Boolean
algebra of cardinality $\kappa$. It exists provided that $\kappa =
\kappa^{<\kappa}$, and is characterised topologically as the unique
$\kappa$-Parovichenko space of weight $\kappa$. Under the Continuum Hypothesis,
$S_{\omega_1}$ coincides with $\omega^*$. This paper investigates questions
related to the Stone-Cech compactification of spaces $S_\kappa \setminus
\{x\}$, extending corresponding results obtained by Fine & Gillman and Comfort
& Negrepontis for the space $\omega^*$.
  We show that for every point $x$ of $S_\kappa$, the Stone-Cech remainder of
$S_\kappa \setminus \{x\}$ is a $\kappa^+$-Parovichenko space of cardinality
$2^{2^\kappa}$ which admits a family of $2^\kappa$ disjoint clopen sets. As a
corollary we get that it is consistent with CH that the Stone-Cech remainders
of $\omega^* \setminus \{x\}$ are all homeomorphic.
