  Many extrasolar (bound) terrestrial planets and free-floating (unbound)
planets have been discovered. The existence of bound and unbound terrestrial
planets with liquid water is an important question, and of particular
importance is the question of their habitability. Even for a globally
ice-covered planet, geothermal heat from the planetary interior may melt the
interior ice, creating an internal ocean covered by an ice shell. In this
paper, we discuss the conditions that terrestrial planets must satisfy for such
an internal ocean to exist on the timescale of planetary evolution. The
question is addressed in terms of planetary mass, distance from a central star,
water abundance, and abundance of radiogenic heat sources. In addition, we
investigate the structures of the surface-H2O layers of ice-covered planets by
considering the effects of ice under high pressure (high-pressure ice). As a
fiducial case, 1M$\oplus$ planet at 1 AU from its central star and with 0.6 to
25 times the H2O mass of Earth could have an internal ocean. We find that
high-pressure ice layers may appear between the internal ocean and the rock
portion on a planet with an H2O mass over 25 times that of Earth. The planetary
mass and abundance of surface water strongly restrict the conditions under
which an extrasolar terrestrial planet may have an internal ocean with no
high-pressure ice under the ocean. Such high-pressure-ice layers underlying the
internal ocean are likely to affect the habitability of the planet.
