  In this paper we present a few properties of $K$-partitions, which are
partitions of Baire spaces such that all subfamilies of such a partition sum to
a set with the Baire property. Among the result proven we have general
existence result that state that the existence of any $K$-partition implies the
existence of $K$-partition of a metrizable space as well as existence of
$K$-partition of a compact space implies the existence of $K$-partition of a
completely metrizable space. We also prove some connections between existence
of $K$-partitions and existence of precipitous ideals as well as measurable
cardinals. There are also outlined possible connection with real-measurable
cardinals, extensions of Lebesgue measure on the closed interval and density
topologies.
