One of the nice things about U.S. immigration law is that children are sometimes included in their parents' petition process. In other words, if you are a U.S. citizen or lawful permanent resident ("green card" holder) who wants to bring a relative to the U.S. on a "family preference" visa, you don't need to file a separate "I-130" petition with U.S. Citizenship and Immigration Services (USCIS) for any children your relative has—you can just list the names of the children on the I-130 that you're filing for your relative.
In immigration law lingo, the child is a "derivative"—someone who derives the ability to immigrate from someone else, without the need to apply separately. (See When Children Can Immigrate to the U.S. With Their Parents, as ‘Derivatives' for details on who qualifies as a child.)
After the I-130 is approved, each family member must apply for the actual U.S. entry visa separately. But at least the whole family can immigrate at the same time if they want to. But what about children you couldn't list on the I-130 because they weren't born or otherwise added to the family yet? They are not out of luck, though extra paperwork might be required, as this article will discuss.
Your relatives might be waiting for a visa for several years after the I-130 is approved, due to the annual quota on "family preference" visas. It's entirely likely that they might have a child during this time.
If a child is born outside the U.S. after the I-130 was approved, do you need to file another I-130, for the new child? If so, that would not be good, because the filing date of an I-130 determines when a visa becomes available, based on what's called the "priority date." A later I-130 would mean the newborn probably wouldn't be able to immigrate until later than the rest of the family.
Fortunately, the law takes care of you in this situation. Any child born to your relative before your relative is admitted to the U.S. can get a visa along with the rest of the family, without another I-130 and without any extra wait (if a waiting list has developed in main beneficiary's visa category). When it's time for the family to apply for their visas at the U.S. embassy or consulate, your relative can apply on behalf of the child, showing proof of the birth (a government-issued birth certificate) and the I-130 approval from USCIS.
If your relative was unmarried when you filed the I-130, and then after the I-130 was approved your relative got married to someone with children, can those "stepchildren" immigrate along with your relative? They can, as long they were under 18 when your relative got married. (The new spouse can immigrate, too.)
If your relative adopted a child after the I-130 was approved, the adopted child can immigrate with the family if the child was adopted while under 16 (18 if it's the natural brother or sister of another child your relative adopted) and after the child has been in your relatives' legal custody, and resided with them, for at least two years.
If your relative is the natural mother of a child born out of wedlock after the I-130 was approved, the child can immigrate with the mother. If your relative is the natural father of a child born out of wedlock after the I-130 was approved, the child can immigrate with the father if the father has or had a bona fide (real) parent-child relationship with the child.
If your relative is not the natural father of the child—for example, his wife had an affair and gave birth to a child—or if he is the natural father of a child but hasn't had a bona fide relationship with the child, he can "legitimate" the child so that the child becomes eligible to immigrate with him.
To "legitimate" a child means to acknowledge that a child is legally one's own. Your relative must legitimate the child under the law of the child's residence or domicile, or under the law of the father's residence or domicile. ("Residence" is where the person can be considered to live for purposes of the law, even if they were not there all the time; "domicile" is where the person actually lives.) The legitimation must take place before the child reaches 18 and while the child is in the legal custody of the legitimating parent or parents.
Even though you won't have to file another I-130 if a child is born to your relative after the I-130 is approved, several things could happen that could affect the child's ability to get a visa, either positively or negatively.
Your naturalization: If you're a green card holder petitioning to bring the child's parent (your spouse) to the U.S., you might decide to get your U.S. citizenship after the I-130 was approved. This would change your spouse and the child into your "immediate relatives." You wouldn't have to file a new I-130 petition for your spouse, but you would have to file a new I-130 petition for each child. (See How Spouses and Minor, Unmarried Children of Permanent Residents Can Change Visa Category.) Although it might take a few months for the child's I-130 to be approved, "immediate relatives" don't have to wait in line to get their visas, so getting your citizenship should speed up the immigration process.
Death or divorce of your relative (the parent): The child's ability to get an immigrant visa through the parent will end if the parent dies before the family is able to get visas. The I-130 process will have to begin all over again if there is another U.S. relative who can petition for the child.
If your relative divorces while waiting for a visa, natural children who were born after the I-130 approval are not affected, but stepchildren who came into the family after the I-130 approval might be. Divorce usually ends the stepchild relationship, so the children of your relative's ex-spouse will lose their ability to get visas through your relative, unless the stepchildren can establish that they have an ongoing relationship with your relative.
The child "ages out": For some relatives of lawful permanent residents, the wait for a visa can be many years. It's even possible that your relative has been waiting so long for a visa that a child born after the I-130 was approved is now over 21! Unless the child fits the criteria to be legally considered younger than 21 under the Child Status Protection Act (see How the CSPA Helps Family-Based Preference Relatives and Derivative Beneficiaries), the child will not be able to get a visa through your relative.
The child gets married: Marriage is another way for the child who has been waiting a very long time for a visa to lose "child" status and the ability to get a visa through your relative. It's very important to tell the child, if they still want the immigrant visa, to not get married until after the visa has become available and the child has entered the U.S. and become a permanent resident.
If dealing with these legal permutations is confusing you or has you worried that someone in the family might lose their chance to immigrate along with other family members, consult an experienced immigration attorney in the United States.