Investigators believe Shazer Limas, 31, murdered Arlet Contreras and their two young sons last month. Contreras' body was found in La Puente, but they haven't found the boys' remains.
Authorities spent several days searching a landfill in Brea and Irvine, but didn't find any sign of the boys - 2-year-old Fernando and 4-month-old Emmanuel.
Limas was arrested on May 3 after leading police on a pursuit that started in the city of Santa Ana. He stopped and surrendered at the San Clemente Border Patrol checkpoint.
The district attorney's office believes Limas killed his family at their apartment in the city of Orange on April 14.
Limas is due back in court June 5. He has been charged with three counts of special-circumstance murder for committing multiple murders. The special circumstances makes Shazer Fernando Limas eligible for the death penalty. The district attorney will decide at a later date whether to pursue the death penalty in this case.