If only one parent is being deported, the child can remain with the parent who is still in the United States.
If there is no parent remaining in the US, the parent(s) may (if the immigration law of the country they?re being removed to allows) take their child with them, may leave the child in the US in the custody of a friend or relative, or may choose to abandon the child in the United States.
All of these outcomes occur. A problem that can arise is that, in some cases, the child may not be permitted to join their parents in the country their parents have been deported to as the child may not be a citizen of that country and may not be eligible to be considered an immigrant. (This is happening with increasing frequency with Mexicans: if the parents never registered their child?s birth with Mexico, Mexico may not recognize the child as a Mexican citizen and will not allow the child to enter Mexico.) With the recent increase in expedited removals, parents have been forcibly separated from their children with no opportunity to make arrangements for their children?s care, resulting in many children being placed into temporary state custody.
At the moment, there is something of a spat between the Department of Homeland Security and the State of California over how to handle children whose parents are deported, especially when the deportation occurs in such a manner that the parents do not have enough time to make arrangements for the custody of their minor citizen child. DHS policy is that states should terminate the parental rights of these children ?promptly? for abandonment and move to place them for adoption. The State of California considers these children to have been ?involuntarily separated? from their parents and places them in temporary state custody with an eye toward eventual reunification, on the grounds that the separation is due to ?circumstances beyond the parents? control?, the same status they?d use for a child whose parents were separated from the child by a disaster or a medical emergency, and thus carries no presumption of parental unfitness and no basis for termination of parental.