It's my understanding that the population cap is a hard cap on the number of adults your fort can have. And once you reach that point births and migrants both stop.
Please don't spread false information.
In my current fort, the pop cap is set to 50. The last migrant wave I got, at year 2 or something, increased my pop from something like 40 to 60. Now my fort reached 12-13 years old, with 113 pop and about half of them babies/children. I still have births from time to time, there's 6 couples with up to 13 kids each. This is very exciting, because kids are starting to become peasants and FINALLY WORK! Or party, since each child is friend or acquaintance with every other child and many adults, and has social skills at professionnal level.
Look into the d_init.txt file. There's the population cap :
You can set the maximum population of your fortress here. Keep in mind that your population must be at least 80 to get a king and 100 to obtain the current game features.
[POPULATION_CAP:50]
Note that the comment isn't true anymore, a king needs 140 population.
And there's the birth cap :
This allows you to control the number of babies+children in your fortress. The first number is an absolute cap on the number of babies+children. The second is a percentage of the current number of adults in your fortress (the default is the essentially meaningless 1000% here). The lower number is used as the cap. The cap only prevents further pregancies, so migrant children, multiple births and existing pregnancies from old saves can still push you over the cap. Setting either number to zero will disallow pregnancies in the fortress.
[BABY_CHILD_CAP:100:2000]
Also, this is with v.31.18