The Travis County Sheriff's Office had been looking for Gabriella Garcia, 10, Julian Garcia, 7, Sebastian Garcia, 3, and Giovanna Garcia, 2. The four children were believed to have been abducted early Sunday.
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Authorities had also been looking for Cesar Giovanna Garcia, 32, in relation to the case, but it wasn't immediately clear if he was detained.
The case was turned over to Child Protective Services, according to the Travis County Sheriff's Office.
Certain criteria need to be met in order for law enforcement to issue an Amber Alert for a missing child age 17 or younger.
First, there needs to be a reasonable belief by law enforcement that an abduction occurred. Additionally, the law enforcement agency believes that the child is in imminent danger of serious bodily injury or death.
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Another criteria is that there is enough descriptive information about the victim and the abduction that would assist in the recovery of the child, such as a vehicle description or license plate number.
As part of the Amber Alert, the child's name and other critical date elements, including the child abduction flag, are entered into the National Crime Information Center.
The Amber Alert system, used in all 50 states as well as the District of Columbia, Puerto Rico and the U.S. Virgin Islands, was created in 1996. It stands for America's Missing: Broadcast Emergency Response and was created as a legacy to 9-year-old Amber Hagerman, who was kidnapped while riding her bike in Arlington, Texas, and later murdered.
You can view all active Texas Amber Alerts from the Texas Dept. of Public Safety here.