  Recent studies have suggested the possibility of Hycean worlds, characterised
by deep liquid water oceans beneath H$_2$-rich atmospheres. These planets
significantly widen the range of planetary properties over which habitable
conditions could exist. We conduct internal structure modelling of Hycean
worlds to investigate the range of interior compositions, ocean depths and
atmospheric mass fractions possible. Our investigation explicitly considers
habitable oceans, where the surface conditions are limited to those that can
support potential life. The ocean depths depend on the surface gravity and
temperature, confirming previous studies, and span 10s to $\sim$1000 km for
Hycean conditions, reaching ocean base pressures up to $\sim$6$\times$10$^4$
bar before transitioning to high-pressure ice. We explore in detail test cases
of five Hycean candidates, placing constraints on their possible ocean depths
and interior compositions based on their bulk properties. We report limits on
their atmospheric mass fractions admissible for Hycean conditions, as well as
those allowed for other possible interior compositions. For the Hycean
conditions considered, across these candidates we find the admissible mass
fractions of the H/He envelopes to be $\lesssim$10$^{-3}$. At the other
extreme, the maximum H/He mass fractions allowed for these planets can be up to
$\sim$4-8$\%$, representing purely rocky interiors with no H$_2$O layer. These
results highlight the diverse conditions possible among these planets and
demonstrate their potential to host habitable conditions under vastly different
circumstances to the Earth. Upcoming JWST observations of candidate Hycean
worlds will allow for improved constraints on the nature of their atmospheres
and interiors.
