  The water content of magma oceans is widely accepted as a key factor that
determines whether a terrestrial planet is habitable. Water ocean mass is
determined as a result not only of water delivery and loss, but also of water
partitioning among several reservoirs. Here we review our current understanding
of water partitioning among the atmosphere, magma ocean, and solid mantle of
accreting planetary embryos and protoplanets just after giant collisions. Magma
oceans are readily formed in planetary embryos and protoplanets in their
accretion phase. Significant amounts of water are partitioned into magma
oceans, provided the planetary building blocks are water-rich enough.
Particularly important but still quite uncertain issues are how much water the
planetary building blocks contain initially and how water goes out of the
solidifying mantle and is finally degassed to the atmosphere. Constraints from
both solar-system explorations and exoplanet observations and also from
laboratory experiments are needed to resolve these issues.
