The couple, Ina Caterina Remhof, 26, and Sascha Schmidt, 24, were picked up on Thursday in a forest near Aosta, where they left the mother's children in a pizzeria after telling the manager they were stepping out for a cigarette.
When Remhof and Schmidt didn't return to the restaurant, police discovered they had left their personal documents in their vehicle and fled the area. The Italian authorities feverishly patrolled borders, train stations and airports to find the couple.
Remhof, who media reports say left the children because she didn't know how she would manage to feed them, has not yet seen her children – who range in age from 10-months to 4-years-old.
A district court in Lennestadt conducted an emergency proceeding to deny the 26-year-old mother Remhof custody while she was still missing, news magazine Der Spiegel reported. Their biological father is in prison, convicted of shaking a baby to death in 2006, the magazine said.
Meanwhile her boyfriend Schmidt remains in police custody after it was revealed that he was a fugitive. According to the Siegen district prosecutor's office, Schmidt is supposed to be serving a long sentence for blackmail. He did not return from a two-day parole from prison in early April, authorities said.
Italian authorities have filed charges against Remhof for abandoning minors, meanwhile German prosecutors have said they will not file charges until they complete their investigation.