Wiktionary
n. An arrangement whereby only one parent has physical and legal custody of a child while the other parent has visitation rights.
Wikipedia
Sole custody arrangements have generally been considered a traditional form of custody for many in the past; however, there has been a trend since the 1980s towards joint custody arrangements being more favorable. Sole custody consists of an arrangement whereby only one parent has physical and legal custody of a child.
Usage examples of "sole custody".
The next thing he knew, she hit him with divorce papers and demanded sole custody of Lisa, claiming that a daughter needed her mother and that Chase was always away.
But in present-day England, under the common law, woman can hold no office of trust or power, and her husband has the sole custody of her person, and of her children while minors.
He wouldn't be showing up until the next to last minute, so she had almost an hour to kill--and to remain in sole custody of approximately two hundred and fifty thousand very hot, very bloody dollars.