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The parents of six-day-old Eliza-Mae, who is thought to have been killed by the family dog, said they will "cherish the little time we were able to share with her".
Eliza-Mae Mullane was airlifted to the University of Wales Hospital in Cardiff yesterday after what is thought to have been an attack by the family's Alaskan malamute dog.
"Even though she was an important part of our family for such a short period of time, Eliza-Mae will always be in our hearts and thoughts and we will cherish the little time we were able to share with her," Sharon John and Patrick Mullane said in a statement.
"She was a dearly loved daughter, sister, granddaughter and niece. She brought joy into our family, and losing her like this has cast the most horrible shadow over all of us.
"There are no words we can use to describe what we feel at the moment, and we don't think there ever will be."
The Alaskan Malamute, the breed of dog seized from a family home following the death of a six-day-old girl, are large and powerful, but have kind and affectionate natures, according to an expert from The Kennel Club.
"They often live in family situations and are extremely loyal," Bill Lambert, the club's health and breeder services manager said.
He confirmed that the breed is not listed under the Dangerous Dogs Act, adding:
The Alaskan Malamute is a Husky-type dog "bred originally for pulling sledges, and they weigh, fully grown, something like 75 to 85 pounds."
Neighbours have been re-living the horrific events here this morning as the emergency services battled to save Eliza-Mae's life - she was just six days old.
She had spent the first three days of her life in an intensive care unit. She only came home at the weekend and spent two nights in the nursery inside the house.
The joy of homecoming for her parents Patrick and Sharon shattered in a matter of moments this morning.
Police have seized the family's pet dog - it is an Alaskan Malamute like the one pictured here. It is not a banned dog under the Dangerous Dogs Act.
Police are awaiting the results of a post-mortem examination, but what is clear is that this community is in shock tonight at what has happened.
Dyfed Powys Police said they are "not in a position to confirm the exact cause of death" of a six-day-old girl who died at a property in a Carmarthenshire village
Eliza-Mae Mullane's death prompted police to seize the family's dog, which was an Alaskan Malamute.
A police spokeswoman said: "The police investigation is ongoing. We are not in a position to confirm the exact cause of death or the injuries to the baby at the moment.
"We are not going to speculate on reports from people in the community and we respectfully ask that you wait for the investigation to run its proper course."
Chief Inspector Ieuan Matthews, of Dyfed Powys Police, said specially-trained family liaison officers are supporting the family of a six-day-old baby girl, found dead at a property in Pontyberem, Carmarthenshire.
"As you can imagine, the family are hugely distressed," he said.
Police have confirmed that the Alaskan Malamute dog seized in connection with the death of a six-day-old baby in Carmarthenshire is not listed under the Dangerous Dogs Act.
Alaskan Malamutes were originally bred as sled dogs for work in the Arctic, but are now popular as family pets.
A six-day-old baby girl whose death prompted police to seize the family dog was named by Dyfed Powys Police today as Eliza-Mae Mullane.
Police have confirmed that the infant who died at a property in the Carmarthenshire village of Pontyberem this morning was a baby girl aged six days old.
The Welsh Ambulance Service has confirmed it attended a property in Pontyberem this morning.
The chairman of Pontyberem Community Council has spoken out following the sudden death of a baby in the village this morning.
Mr Lewis described Pontyberem as an "ex-mining community village" with a population of 2,500 - 3,000.