There is definitely a boundary, but not a hard limit. The game looks at the ratio of provinces to adult male family members. If the number is too low, you start getting adoption opportunities. If the number gets too high, your family stops having children. Only when the number drops below the upper limit do new kids start being born. Any children can still come of age during that time, daughters can get married, princesses can bring in new generals, and "man of the hour" can still happen, but no new kids will be born.
In both my Spanish campaign and my Venice campaign I ran up against this. At game start I had the default family. I quickly expanded, got a few adoptions and marriages and children reaching majority. The third generation of the family was large, and as a result the fourth generation was HUGE! Of course, the fourth generation didn't have kids as a result, so I went through a long period where I had mass numbers of barren couples. Only when the fourth generation started to die off did things get a little better. There were time periods when I was down to 4 generals, because the kids weren't old enough yet and the old guys were dropping 3-5 every turn due to old age, and I can only get one adoption per turn. Of course, the fifth generation had dozens of kids, meaning the 6th generation was huge and had no kids as a result, so it happened again. 7th generation recovers, 8th generation is huge, repeat ad infinitum.
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