  Terrestrial exoplanets in the canonical habitable zone may have a variety of
initial water fractions due to random volatile delivery by planetesimals. If
the total planetary water complement is high, the entire surface may be covered
in water, forming a "waterworld." On a planet with active tectonics, competing
mechanisms act to regulate the abundance of water on the surface by determining
the partitioning of water between interior and surface. Here we explore how the
incorporation of different mechanisms for the degassing and regassing of water
changes the volatile evolution of a planet. For all of the models considered,
volatile cycling reaches an approximate steady-state after $\sim 2 \
\mathrm{Gyr}$. Using these steady-states, we find that if volatile cycling is
either solely dependent on temperature or seafloor pressure, exoplanets require
a high abundance ($\gtrsim 0.3\%$ of total mass) of water to have fully
inundated surfaces. However, if degassing is more dependent on seafloor
pressure and regassing mainly dependent on mantle temperature, the degassing
rate is relatively large at late times and a steady-state between degassing and
regassing is reached with a substantial surface water fraction. If this hybrid
model is physical, super-Earths with a total water fraction similar to that of
the Earth can become waterworlds. As a result, further understanding of the
processes that drive volatile cycling on terrestrial planets is needed to
determine the water fraction at which they are likely to become waterworlds.
