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I mean no asteroid, planetoid that I am aware of has water on its surface. It is way more common to see ice in it. So I figured that the size of the celestial body has something to do with the cycle of water. Does this theory hold true? Do exoplanets with water have to be similar size than Earth? To have water does it has to be a rocky planet?
I mean some moons have water inside their crust (I think). Some planets seem to have had water before, like Mars.
Liquid water can't exist in a vacuum. If there is no pressure, then the boiling point will drop to the freezing point and so there will either be ice or water vapour.
And if the world is "small" then its gravity won't hold on to any water vapour, and it will be lost to space. The Earth can have liquid water because its gravity is strong enough to hold onto water vapour, and provide vapour pressure to raise the boiling point to 100 degrees, which is hotter than the temperature due to the sun.
A small world can have a sub-surface water layer, as the ice above it will stop the water from boiling off into space. Enceladus has such a layer, but if Enceladus was a moon of the Earth, the sun would have melted the ice and the water would have boiled off long ago.
Do celestial objects need to be big to have liquid water on their surfaces?
Yes.
In a nutshell: liquid surface water needs an atmosphere. To sustain an atmosphere, a planet must be sufficiently massive, therefore sufficiently large. The warmer a planet, the more mass it needs to sustain an atmosphere. A planet warm enough for liquid water must thus also be large enough to sustain the atmosphere for this liquid surface water to survive.
Liquid water can only exist if pressure is larger than 612 Pa. The boiling point depends on the pressure. At a pressure of 101 kPa, like average conditions on Earth sea level, the boiling point is 373 K (100 °C). At a pressure of 34 kPa (average on the summit of Sagarmatha/Mount Everest), the boiling point is 71 °C:
Source: Cmglee, Wikimedia Commons
For liquid water to exist at the surface, a sufficiently thick atmosphere must exist to provide this pressure. It could be a little thinner than on Earth, but if it's too thin then water might boil all too easily.
Mars has an average surface pressure of 636 Pa on average, which means that in theory, liquid water could barely exist, but only when the temperature is pretty much exactly 273 K (0 °C). One degree colder and it will freeze, one degree warmer and it will boil. In reality surface temperature on Mars is on average 210 K. The pressure on Mars depends on the location, but for future Mars colonists, it should be fun challenge to try to see how long they can make liquid water survive (heated, but unpressurised) at some of its lowest points!
To retain an atmosphere, a planet must have sufficient gravity. If there is not enough gravity, most of the atmosphere will drift off into space due to thermal effects (molecular thermal velocity in excess of escape velocity, see below), solar wind escape (charged particles pushing against the atmosphere), and other (smaller) effects. Worse, not only is most of the atmosphere lost if a planet is too small, but the lighter species such as water are lost more easily than, say, carbon dioxide. So not only must gravity be sufficient to hold onto an atmosphere, it must be sufficient to hold onto water specifically. The only way to counter or prevent losses to space are sufficient gravity (reducing loss) or a constant new supply. The size a planet needs to have to retain an atmosphere depends on temperature:
Source: Cmglee, Wikimedia Commons
To have sufficient gravity, a planet must have sufficient mass. To have sufficient mass, it must be sufficiently large. How large is "sufficiently large"? That depends on the temperature. Titan is quite small, but also very cold. At temperatures warm enough to sustain water, a planet could be a little smaller than Earth, but not much. Mars is too small. Although a Mars-sized planet at an Earth-like temperature could theoretically retain a Titan-like atmosphere of mostly nitrogen for a while (it'd be close, being a bit larger would be safer), it would still lose its water over time.
To have a constant new supply, a planet or moon would need vulcanism. To sustain vulcanism, a planet needs an internal heat supply, for which it also needs sufficient mass, at least to sustain this long term. A moon can also get energy from a planet to sustain volcanism. Maybe a warmer hybrid between heavily volcanic Io and Enceladus with cryovolcanoes around a hypothetical extrasolar planet could sustain a highly dynamic atmosphere, even if it would normally be too small according to the diagram above. That might be unlikely, though; in case of Io, the same energy source that powers the volcanism also strips away the atmosphere (and Io has the least water of anywhere in the solar system). In any case, the only moon with a significant atmosphere in our solar system is Titan, which is also the smallest body in the solar system with an atmosphere. It's very cold at 94 K; if it were warm enough to contain liquid water, it would lose its atmosphere.
Maybe a very young planet could be quite small, still vulcanically active, and still keep on to enough atmosphere to allow for widespread liquid surface water. There are no such planets in the solar system either, but it could be conceivable for an extrasolar planet. For any planet of significant age, however, only mass, thus only size, will help.
Size does matter.
gerrit's answer has done an excellent job of showing that (1) there are a narrow set of temperatures and pressures where liquid water exists and (2) a planet has to be pretty big to have enough gravity to keep water in the atmosphere. However, I wanted to mention this:
Salt is often poured onto roads in the winter to melt ice, which is effective because salt water has a lower freezing point and higher boiling point (and is more thermodynamically stable) than pure liquid water. For instance, sea water freezes at 271 K (28 °F), which is lower than the freezing point of pure water, 273 K (32 °F). Coolant in cars usually contains water with ethylene glycol added to depress the freezing point and elevate the boiling point.
This figure from Cynn et al. shows that a mixture of 63% water plus 37% ammonia allows liquid water to exist down to 180 K, although it's hard to tell where the pressure cutoff might be at this temperature from this graph. The pressure cutoff goes down temperature, so it's certainly below 100 kPa. You might be able to sustain liquid water–ammonia mixtures at low temperatures and pressures on the surface of Mars-sized bodies or smaller.
Water–ammonia mixtures are thought to be present beneath the surface of many bodies in the outer solar system, including Titan, Pluto, Charon, and Ganymede. Cryovolcanism based on eruptions of liquid ammonia–water mixtures may be more common than not among the terrestrial satellites beyond Mars.
