I am grateful for the varied responses from so many, and especially the fact that there is so much disagreement in them!
I still think, myself, that up to the point when the Earth's surface actually solidified, the bulk of the water on the Earth's surface now was water vapour in the atmosphere. Indeed, the most abundant gas in the atmosphere at that time may have been water vapour. As the surface cooled, the saturated atmosphere would have condensed and very quickly have fallen to the surface to provide the oceans in a very short time. I would suggest that the most common early weather would have been falling rain that never touched the ground for millions of years. As it approached the surface, it would have boiled away again and risen high into the atmosphere to cool and condense again as it rose, in a long cycle that only started to end when the surface was cool enough to tolerate the liquid form. That cycle hasn't finished yet.
I believe, also, that since the planets, asteroids and comets all formed from the same source, the Earth would have naturally started with a representative portion of it. Some asteroids are mostly rocky, some more metallic and some more icy, but the larger the body, the more likely its composition would be to be the mean of the substances found in the part of the cloud in which it formed.
Size would also be a factor, in that larger bodies would be better able to hold on to lighter gases like hydrogen and helium (like the gas giants) than smaller ones. However, the Earth could be of a suitable size to lose the lightest gases and retain somewhat heavier ones like nitrogen, carbon dioxide and water vapour.
I maintain that even if an Earth sized body was molten iron and rock, obviously with no surface water, it does not follow that an atmosphere with a very high water vapour composition is necessarily ruled out. I accept that if a wet comet hit the early Earth that the total amount of water on the planet would increase, but the same would be true about rocky or metallic asteroids contributing more of the materials of which they were composed adding more to the whole.
Evidence of a lot more water having been on Mars in the past seems convincing, and there are many good reasons for there to be less now. Perhaps the early Earth had a great deal more total water when it was first formed, and now we have lost much of it, even more than we ever gained from comets and asteroids, but still retain more of a percentage of the total than Mars has. Venus is another planet that may have had more water at one time but for other reasons has lost most it or had it tied up in a chemical form.
We are in an unprecedented era of discovery of extra solar planets. The more we find, the more variety we find. I suspect they are all as unique as snowflakes or fingerprints only that they come in nearly infinitely more compositions and sizes. I suspect that if copies of the Earth at various different times were examined side by side, we would find it hard to believe it to be the same planet at different ages in its life, without a far better understanding of how planets evolve.
Again, thank you for the replies. It has been much food for thought.