Identical: Abby, Brindabella and Laurel.

Identical: Abby, Brindabella and Laurel. Photo: Supplied

A rare set of identical triplets born in the US, with an Australian father, have become an unexpected global sensation.

The truly one-in-a-million Laurel, Abby and Brindabella, named after the mountain range to the ACT's west, were born to former Canberran Tom Hepner and his American wife Hannah, at a California hospital, in late November.

Doctors put the odds of naturally conceived identical triplets being born without the help of fertility drugs as high as one in 200 million.

Having made front-page news in The Sacramento Bee, the story popped up across the US and in Britain.

''It has been overwhelming, but we knew it would be short-lived. I'm sure our girls will be amazed one day that the rarity of their birth was so celebrated,'' Mr Hepner said.

The triplets are in a neonatal intensive care unit in a hospital in Sacramento, after being born via caesarean at 33 weeks.

All three are putting on weight and progressing beautifully, their parents said.

''I'm in awe of the fact that the girls are here and doing so well,'' Mrs Hepner said. ''Every day I think about the fact that they are still supposed to be incubating inside me. I feel like I've cheated the system and get to meet and cuddle my girls so soon.''

Mr Hepner said: ''Growing up in Canberra, I spent large amounts of time fondly exploring the Brindabella ranges, west of Canberra. It is also where we had our small wedding ceremony in 2007, on top of Mount Franklin.''

The couple moved to the US in 2010. Mr Hepner, 33, works for a mapping and modelling company, and Mrs Hepner, 29, manages a farmers' market.

When they found they were having triplets, Mr Hepner remembered that ''time stood still [those] first few minutes''.

''I think that for most pregnancies, at some point, there is probably a joke about the possibility of twins,'' he said. ''Triplets never ever got mentioned. Obviously it happens in the world, but not to us or anyone we've ever met.

"They are healthy, and very feisty, the nurses say.''

At birth, Abby weighed 1.36 kilograms, Laurel was 1.81 kilograms, and Brindabella was 1.67 kilograms.

The triplets are expected to leave hospital closer to their full-term date, and their parents are now looking to the logistics of going from being a couple to a five-member family.