[GlentoranMark (OP)]

I was gonna ask this question: "What would happen if a planet existed entirely made out of water?" but I guess it boils (no pun intended) down to how water behaves under pressure.

So what would happen to water at the centre of an Earth or Sun sized planet?

[CZARCAR]

makes stuff in my pressure cooker cook faster with less eneergy

[CliffordK]

What about salt?  Other impurities?  Salt, of course, is leached out of rock which you are eliminating.  Are you adding an oxygen/nitrogen atmosphere, or is the atmosphere going to consist entirely of H₂O vapor?

Keep in mind that life on Earth requires water, salt, carbon, phosphorous, nitrogen, potassium, iron, and a number of other elements, without which your water planet would be very sterile.

I'm assuming a surface temperature somewhat like earth's, with cooler poles, and warmer equator. 

The sun as well as gas giants all have some kind of a spin or surface circulation, so I would assume the same for the planet, although I'm wondering if convection forces would force the spin to be synchronized with the solar plane. 

Winds (assuming an atmosphere) would likely be much more circular around the planet in pattern due to not having continents to break them up, and divert them north and south.

Ice would likely form at the poles, in part depending on the axial tilt of the planet.  However, it may not be very stable as there is no anchored rock to hold it in place.

Water has a most unique phase diagram.
http://www.enm.bris.ac.uk/teaching/projects/2002_03/jb8355/review.html

At relatively low pressures (up to what we get at the bottoms of our oceans), the higher the pressure, the more it tends towards liquid.



However, at extremely high pressures, a type of ice will form.



The scale on the chart is logarithmic.

http://en.wikipedia.org/wiki/Orders_of_magnitude_%28pressure%29
According to Wikipedia, the pressure at the bottom of the Mariana Trench, about 10 km below ocean surface is about 100 MPa.  The pressure at the center of the earth is about 3.64 x 10³ MPa.

Keeping in mind, of course, that Rock is higher density than water, so the planet would either be lower mass than Earth, or larger in diameter than earth and with the same mass.

Anyway...
Somewhere around the 10 km depth (Mariana Trench), ice would begin to form. 

If the planet's core is "cold", then there would be a solid ice core.  However, if the core is "hot", then at some point below the ice crust, liquid water will form once again.