Saturated boolean algebras and their stone spaces

For an infinite cardinal κ, we call a compact zero-dimensional space a κ-Parovicenko space if its boolean algebra of clopen sets is κ-saturated and has cardinality κ^<κ. We answer some questions about these spaces which were posed in [14]. For instance, it is shown that a κ⁺-Parovicenko spacé can be a Stone-Cech remainder in a natural way. We show that some of the results in [14] which used the assumption κ^<κ=κ, do indeed require this assumption. We also show that if 2^κ=κ⁺ then each compact F_κ⁺-space with weight κ⁺ can be embedded into a κ⁺-Parovicenko space (and so into an extremally disconnected space).