Nelson Arave, the first and original "Arave," ended up in Nauvoo in 1842, about the age of 10.
How did he end up there?
Nelson's father and grandfather died on May 19, 1835 while rafting logs on the St. Lawrence River.
The simple story is that soon afterward, Nelson's mother felt she could not care adequately for all three of her children and so in about 1835, she "loaned" Nelson to Jesse and Ruth Lampson, who were soon going to resettle in New York, where she was headed. Nelson was only about age 3 at this time.
However, the Lampsons, who had been members of The Church of Jesus Christ of Latter-day Saints, since 1832, didn't end up traveling that way.
They moved with the church to Michigan, where Nelson was baptized at age 8. Two years later, in 1842, the Lampsons (who had two daughters) had moved to Nauvoo with the church.
Given the poor communication at the time, perhaps Nelson's mother did not have the time or resources to search for him. While she had to have known there was a chance she might never see Nelson again, I'm sure she thought about him a lot and would have liked him to be with her.
Meanwhile, the Lampsons did not actually adopt Nelson formally, but he lived with them for more than 15 years,until he headed to Utah territory.