I only got about 2 adoption proposals in over 100 years, and both of them weren't worth bothering with, but I had to accept them because I had too many provinces that had no Governers.
From what I have read about Roman nobility there doesn't seem to be any proof of them not having any kids. Most of them had 2 or 3 kids, precisely to carry on whatever dynasty to which they belonged. That was how they became senators and moved up the ranks, because of who there fathers and grandfathers were.
The only man I can think of who was a "new man" and worked all the way to Consul was Cicero.
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