Rumor claims many things, but proven cases will be impossible to find.
If I were to narrate such a strange event in game, I would have the powers that be immediately claim the child so that it could be "adopted" by the ranking local Uzuz, who would claim it as their own natural birth. A low-ranking, uncooperative mother of such a child might well be killed out of hand - all in the best interest of the child, of course. No Uzko could possibly be expected to raise such a sacred and powerful creature to it's full potential.
If no Uzuz were immediately available, the most powerful local Kyger Litor priestess would claim the child as her own, and, depending on her personal power and piety, either keep it secret as long as possible, raising it herself as proof of her own uzuz status, all the while preparing for war should a group with an acutal Uzuz discover her treachery - or she would contact her closest related living Uzuz and arrange to somehow safely transport the infant to them.
An uzko player hero who gave birth to such a child would face immense challenges, no matter how she played it... keeping the child herself sets her against the entire Kyger Litor hierarchy, and giving it up makes her an inconvenient irritant to the "real" (adoptive) mother, who is powerful, selfish, and does not like being irritated.
This all becomes a moot point, if the "uzko" mother is powerful enough "prove" through heroquesting that she really was an uzuz all along, and thus the baby is her own by right, and it really would not be in the best interest of Anyone to try and take it from her. (grrr! rawr!) But then she'd hardly be a "common" uzko, would she...
In short, if it DID happen, it would not be long before no one living Knew that it had happened, so imo, it is entirely up to Your Glorantha wether such a birth is impossible, or merely uncommon.
Powered by hypermail