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Several relationships other than marriage permit sponsorship for permanent residence:
An adult (over 21) US citizen child can sponsor a parent.
US citizen parents can sponsor a child of any age, whether married or not, though whether the child is over or under 21 and whether the child is married or not can make a huge difference in how long the process takes.
Adult (over 21) US citizen siblings can sponsor a brother or sister, though this process takes such an incredibly long time for immigrant visa availability as to be impractical in most situations as anything but a fallback.
A permanent resident (non-citizen) parent, in addition to being able to sponsor a spouse, can sponsor a minor (under 21) child or an unmarried child over 21, but not a married child over the age of 21.
Grandparents, Aunts and Uncles and Cousins (as well as any more distant relationship) can’t sponsor for permanent residence whether they be citizens or permanent residents themselves.
It is for an adult US citizen child sponsoring a parent and for the other categories where the individual being sponsored entered legally and has maintained valid status (which is unusual) or where the individual being sponsored remains abroad. For someone present in the US without status, these categories may simply not be practical. Adjustment of status in the US would require not just lawful entry (“entry with inspection”) as would a US citizen marriage-based case, but unbroken/unelapsed immigration status right up to the time of filing the final stage. Without this, the person being sponsored would need to Consular Process – go through a US consular post abroad. Here, the act of leaving will often trigger the three and ten-year reentry bars for which a waiver would be needed – and depending on the category, no qualifying relative may be available.