The State's adoption agencies do not know what happened to thousands of babies for whom adoption files were opened but never completed.
But the Adoption Authority of Ireland (AAI) has said a full review of these files is "not feasible" as it would be extremely costly and would put a significant burden on staff.
The AAI holds more than 4,000 incomplete files, mostly dating from the 1950s and 1960s, while Tusla has over 70,000 files but cannot say how many of these are completed adoptions or partial files.
"The only way to categorically say what happened in every single instance would be for a forensic review of each and every adoption file and record including incomplete adoption records," said AAI chief executive Patricia Carey.
"It's not possible to say what happened without a full review. And that in my view is not feasible, unless you are to close out all other services it would take years," she said.
It comes after a sample review of illegal birth registrations found there could be potentially up to 20,000 suspicious cases.
This review, which examined 10% of the incomplete files held by both Tusla and the AAI, was tasked with looking for markers which would suggest a birth was illegally registered and was not asked to find out what happened to the children involved or to establish if an explanation was given for the lack of an adoption order.
Tusla told the independent sample review that the exact number of records they hold in respect of adoption societies or other categories of agency is unknown.
Children's Minister Roderic O'Gorman has not ruled out full investigation into illegal birth registrations and related issues, however, he has said he will be guided by the work of Professor Conor O'Mahony, the special rapporteur on child protection, who has been given six months to make recommendations based on the sample review
However, the AAI is concerned that a full-scale forensic review of the incomplete files they hold would take many years and even the number of files that exist is unclear.
"Because all adoption files and records are not in the one location and because there has never been a full forensic review of every adoption file and record, you're never going to be able to say categorically it's 4,000 or 5,000 or whatever," said Ms Carey.
She said adoptions may not have been fully processed for a number of reasons, for example the child could have sadly died; the parents or parent may have decided to keep the child; or a relative may have decided to take care of the child.
"There's a whole range of things that could happen.
"When I say an incomplete adoption file, it could be just something as small a letter from a birth folder saying: 'I want to give up a child for adoption, who can I talk to? Here's my name and address.' So, it would vary, it would go from that to the adoption process starting and even going the good way down the process.
"Given the type of records that were kept, particularly in the earlier stages, the '50s and '60s, it wouldn't always be clear what exactly happened," she said.
A Tusla spokesperson said the child and family agency holds "well in excess of 70,000 records relating to adoptions and other alternative care records".
"We open files/records only when we receive an application for a service. We do not routinely search these records looking for indicators or proof of illegal registration or other information."
The spokesperson said Tusla's core function is to deal with requests for personal information from individuals on records that they hold, and also when requested and to support the search and reunion of birth relatives.