Authorities are looking for the couple who last paid rent on the unit in 1994 and are believed to have since moved out of state, Graham County Sheriff Frank Hughes said Thursday. He declined to reveal the couple's names.
One of the bodies was found Monday by Thomas Bright, 58, who had paid $75 for the contents of the abandoned unit - a crib, stroller and 40 to 50 boxes - at an auction Saturday, hoping to find forgotten treasures.
"There was a comforter and bedspread in there and off to the side was a little cardboard box and I figured there was something good in that so I opened it up," said Bright. "I could see the back of the skull and the unclothed hole in the top of the head... I pushed the bag down a little bit further and I could see the eye and the lips so I just closed it back up."
Bright called authorities, who discovered the remains of the other children: one in the same box as the first and the other in another box.
The bodies had been in one of about 50 haphazardly constructed sheds nestled in a dilapidated part of Safford, an eastern Arizona town of about 9,000.
Each child was a newborn or nearly full-term fetus, but investigators have not been able to determine whether any were born alive. Medical examiners also have not determined the babies' gender or whether they are related.
Pima County chief medical examiner Dr. Bruce Parks said the remains were primarily bones and dried skin.
"Establishing identity is going to be very difficult. We're really dependent on information about what happened," Parks said.
Hughes said investigators believe the children may have been dead for eight to 10 years. No infants were reported missing in the area during that time, but area residents have been calling police with leads.