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Were the thirds carrying eggs from donors, or would the children really be half-artificial?
The children are apparently normal humans. It never really explains how this works.
Most likely, the Thirds are like the humanoid Cylons - constructed with both artificial parts (likely their skeletons and nervous systems are artificial, and possibly augmented with greater physical strength and stamina than the average human) and organic tissues (everything else, especially the "plumbing").
How does a Third experience childhood? Wouldn't simulating a human's maturation involve multiple painful operations to extend or outright replace huge sections of their bone structure? Wouldn't that be exceedingly traumatic and leave extensive scarring?
Well considering you only see a handful(around 5 I think) running around it's hard to tell until the end when Armitage runs into her creator again. It appears they were entirely artificial cyborgs in that they used organic tissues and aren't humans being converted into cyborgs. I think that was the reason why there was such hostility from the humans.
Actually the answer to this question lies in the character of Julian Moore: Whereas all the other Thirds are adult females, he is a child and a boy, and although it's questioned there's no definitive answer as to why he was made an exception. What matters here is that Thirds do not age. Julian has always been a boy, as presumably Armitage as always been a young woman. The children the Thirds are capable of giving birth to, on the other hand, as the question answerer above points out, are seemingly completely human and don't have mechanical parts needing operated upon.
Probably all the thirds were carrying either human eggs or some artificially created equivalent (ie a cell created from scratch by synthesizing the DNA, proteins, lipids, etc, and assembling it into a functional egg), or alternately, the thirds can make this artificial cell in their bodies (If their reproductive cycle is exactly analogous to that of a human, then it would take about a month to manufacture each egg). The genetic template presumably would have to have originally come from some human donor.
"Some kind of academic dominance game was going on. Those can get nasty. I think some of their theories got sent and some got buried. Numbers, too. One theory had to do with the endocrinal flux in the uterus. The numbers we got suggest that the actual ebb and flow of biochemical products as the mother is awake, asleep, afraid, hungry, tired, sexually stimulated, whatever...is a form of communication between mother and child. It's another nutrient...an emotional nutrient, if you will, as important as blood or oxygen. When you try to create a computer program to simulate the messages that a mother sends to her child, you have to remember that it is a feedback loop between the mother and the fetus. Thousands of fetuses were studied, and the ways that their mothers responded to them were recorded, and a refinement of everything that was learned was created for use in the creches. Except a camel is a horse designed by committee. There is a difference between the clumsy elegance of the human body and the sophisticated, intellectual choices made by a committee of experts deciding which endocrinological experiences are good for baby. They tried to round out the experience. This mood swing was inappropriate, that orgasmic response pattern was a biochemical form of child abuse, a mother experiencing anger is damaging her child. The liberals swung the profile one way, the conservatives another. Too many morphemes. Too much adrenaline. Chill those kiddies out."
And the end result is not only a sociopath, but a megalomaniac. I imagine the Martian authorities tried to grow babies in beakers but the only method that worked was plugging them into AIs. The next logical step was, "Hey! We have smart sexbots, just put the plumbing in them!" Thirds are basically reverse-Hollywood Cyborgs - a synthetic brain with human plumbing instead of a human brain in a synthetic casing. Pluto notes that "That's why the Thirds were made to be so human, not just physically, but emotionally. It takes more than the right plumbing to procreate." They grew the soft parts in a beaker(one of which is seen in the final scenes of the series, in Dr. Asakura's lab on Dunwich Hill), and stuck high-end AIs in their skulls.