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The space $S_\kappa$ is the Stone space of the $\kappa$-saturated Booleanalgebra 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 questionsrelated 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 acorollary we get that it is consistent with CH that the Stone-Cech remaindersof $\omega^* \setminus \{x\}$ are all homeomorphic.

The Stone-Cech compactifications of $\omega^*\setminus \{x\}$ and $S_\kappa\setminus\{x\}$