A two-year probe to find the mother of a newborn baby who was abandoned in a Tesco bag for life has "explored and exhausted" all lines of inquiry.
The baby boy was found outside the vicarage of St Peter's Church in Bramley, Leeds on 23 November 2016.
He was taken to hospital by ambulance but later pronounced dead.
Two years on from the discovery, police have appealed for the mother to come forward and arrange the baby's funeral, stressing she was "not in any trouble".
The boy was found near the doorstep of the vicarage wrapped in a blue striped towel and a white, 15in collar man's shirt made by Dunnes at about 09:00 GMT.
Forensic examination of the shirt showed it had been regularly worn by a female, officers said.
A DNA profile was recovered from the shirt but is not recorded on the police database.
His death has not been treated as suspicious and the boy's body has been retained as detectives liaise with the coroner's office.
Det Supt Nicola Bryar, who led the investigation, said: "Sadly we have now explored and exhausted all the available lines of inquiry without being able to identify the mother of this baby boy.
"Our discussions with the coroner's office will include when her son's body can be released for a funeral.
"That is something we would like her to be able to lead the arrangements for, and to have the chance to say goodbye properly.
A new dedicated mobile phone number (07881 894505) has been set up for the mother or anyone who knows who she is.