'boiling off' seems like a bit of an oversimplifiction - yes, intuitively, hot water vapor rises - when it's surrounded by cooler denser gases. So I get that if you have a cloud of various atoms and molecules orbiting a sun that is accreting together under gravity, the iron is going to end up at the core of the body that forms, and the light stuff like H2O is going to be a big fuzzy cloud round the outside; but it's not going to 'evaporate' off somewhere else, surely? If the Earth's hot, you wind up with a ball of molten iron, surrounded by a cloud of water vapor (and O2, and N2, and so on). Once the Earth cools, that vapor seems like a good source for liquid water, no need to bring it back from the Oort cloud in comet form. Unless 'boiling off' the water means that it disappears from Earth's orbit altogether... Is the idea that it gets blown out into the outer solar system by the solar wind, or just that the sun gives that cloud of water vapor so much energy that it's able to diffuse out of Earth orbit? Doesn't the same logic apply to the other lighter substances like oxygen, nitrogen, methane... so did they come back from comets too?

>>> yes, intuitively, hot water vapor rises

Temperature is just an expression of mean kinetic energy of particles. If gases (especially light gases) are hot enough, their kinetic energy can correspond to a velocity that actually exceeds the escape velocity of Earth's gravitational well. This is how hot gases can be removed completely from the Earth's atmosphere (and then solar wind & radiation take care of removing it from there). Even at today's atmospheric temperatures, helium gas (molecular weight of 4 atomic mass units, much lighter than molecular oxygen, nitrogen, etc.) can escape from Earth's atmosphere.

Right, that was my thinking; so does the same not apply to nitrogen, and methane (which I think both have lower molecular mass than water)?

(EDIT: actually, on second thought, N2 would have a higher molar weight than H2O...)

Yes on your edit. The origin of Earth's atmospheric nitrogen is thought to be in part due to outgassing (in other words, gas that was stored inside rocks in the early Earth and then released from inside), but is highly uncertain & debated. It's actually so poorly constrained that it may end up being my PhD thesis topic (astrophysics and origins of planetary systems). So not even the experts know, yet, although cometary delivery in cyanide ices from comets is a leading hypothesis (similar to the delivery of water ices).

Was digging around and found some good info, looks like tomr already answered the Nitrogen part of the question, which is the same info I found.

As far as methane, it seems to all mostly be biogenic[1].

[1] - http://www.astrobio.net/news-exclusive/methane-on-earth/

Solar radiation splits water into hydrogen and oxygen at high altitudes. The hydrogen is then light enough to escape, driven by more solar radiation.

Although that explanation makes intuitive sense, it seems to be based on a massive overestimation of the amount of H2O that currently exists on Earth. A thin layer of water covering two thirds of the surface is not much compared to the entire mass of the Earth.

Isn't it possible that early Earth contained many times as much H2O as it does now (like some of those Jovian satellites that are covered in hundreds of miles of ice), and what we have now is simply what's left after the majority "boiled off"? That way, there would be no need for comets and asteroids to return the lost water to Earth.

Other comments in this thread mention vast amounts of water trapped deep inside the Earth, as well as outgassing of nitrogen after the Earth has cooled down. Perhaps the water near the surface of the early Earth did "boil off" entirely, but what we have now is the result of subsequent outgassing?

Very much what I was going to suggest, as well. But I think that would mean the Earth formed in the outer solar system and migrated inward later. Not sure if there is any evidence compatible with or contradicting that.