Whether an Olivia, Asher or an Arya, there's one born every minute, but for some the journey is a long one. "Erik and I are so proud and happy to welcome to the world our much longed-for addition to our family and our first son," Net-a-Porter founder Dame Natalie Massenet wrote on Instagram this week.
"Jet was born on September 15 in Los Angeles and came into our lives with the most generous help from our surrogate."
But parents such as Massenet (52) who want to have children this way far outnumber the surrogates themselves. "Demand is on the increase," says Dr Suvir Venkataraman of the Harley Street Fertility Clinic. "But one of the limiting factors is actually finding surrogates." Need, he says, far outstrips supply.
Partly this is because it's illegal to advertise for a surrogate in the UK (though shadowy sites exist). "Between 80 and 90% of people going into these extraordinary relationships are therefore strangers at first," says Dr Nick Raine-Fenning, an associate professor of reproductive medicine at Queen's Medical Centre in Nottingham (the other 10% being between friends or family).
Instead, only Britain's three non-profit agencies can help couples find a match: Brilliant Beginnings, Surrogacy UK and COTS (the last is in fact so over-subscribed it's not currently accepting new applications).
There's the American option, where paid surrogacy is both legal and prevalent in many states and where many large surrogacy agencies say international clients provide the bulk of their business (there are more than 2,000 babies born through gestational surrogacy in the US every year, while Thailand and Mexico are also popular destinations).
International would-be parents face stumping up between £120,000 and £140,000 in the US. Here, the going rate is between £12,000 and £18,000 to cover expenses.
According to Helen Prosser, co-owner of Brilliant Beginnings and legal practice NGA Law, the intended parent is legally obliged to cover the surrogate's expenses but much larger figures can be approved by the magistrate for money lost in earnings and further costs. IVF can cost between £8,000 and £12,000 per cycle.
Yet "money is never the starting point", argues Raine-Fenning. "It's not a fertility treatment. It's specifically for people who can't conceive a child of their own."
Naturally, this is unlikely to put off those who are willing to exhaust their options. "The actual number of people looking in the UK is huge," says Prosser. Although there were only 350 parental orders (the legal paperwork needed to adopt a surrogate child) in 2016, Prosser argues this is the tip of the iceberg. Nevertheless, none of the NHS's Clinical Commissioning Groups currently fund surrogacy.
Around 40% of Brilliant Beginnings' client base are gay men in same-sex relationships, while around half are straight couples who "have had years of failed IVF" or cannot carry a child for medical reasons, such as having had chemotherapy.
Then there are older people who want a second try at a family or met their partner in later life. Former Serpentine Gallery director Julia Peyton-Jones became a mother for the first time earlier this year at the age of 65, although it is not known if she used a surrogate. Prosser adds: "We've got single dads and some single women, although very few, who just haven't met the right person and want to have a child on their own."
Two types of surrogacy exist. In traditional surrogacy the biological mother carries a surrogate's egg which is inseminated with the father's sperm. This can be done either at home, using a donor insemination kit, or in a clinic. With gestational surrogacy, where the surrogate carries a baby she is not genetically related to, the egg from the intended mother or donor is fertilised through IVF and then placed inside her at a fertility clinic.
If cost makes surrogacy prohibitive, the rarity of that "most generous help" is also a stumbling block. Caroline Evans, a 35-year-old care assistant in a residential home for people with dementia, has been a surrogate twice through Surrogacy UK, and is currently trying for a third (she has her own daughter, Aimee, 12). "Desperate to be pregnant again" but not wanting more children of her own she signed up to Surrogacy UK as a potential surrogate. "I also felt like I was wasting my fertility by not helping others to have a child - if I could help, why not?"
Evans had to submit a GP's report confirming her good health, and a clean criminal record, while an experienced surrogate from the agency visited her to confirm her home was suitable (this is standard across all three agencies). There was a minimum three-month "getting to know" period with a couple she met on the agency message board.
"We had a great time building our friendship, we met each other's families and, after an 'agreement' session with a mediator, we started inseminations - it took four months for me to get pregnant," says Evans.
"A big misconception is that in surrogacy the baby is 'handed over'. I have had two surrogate babies now, and at no point have I handed a baby over - the first couple's little girl was born on to my tummy, the three of us were gathered round looking down at her, she held her mum's hand, and we all congratulated each other. That little girl is three this weekend, so my mum and I are going to see them and join in the celebrations."
This strong bond between intended parent and surrogate, Prosser says, is typical. "They're on this two-year journey together. It's almost unnatural for them not to have some sort of relationship afterwards."
Can parents insist on changes in lifestyle for the surrogate as they carry their child? This is a grey area. Although Brilliant Beginnings insists expectations are meticulously set out between parties (they also stipulate counselling for all) surrogacy contracts are not legally enforceable. The child belongs to whoever carries it until the parental order is signed at a magistrates' court after the birth.
"There have only been three cases published in the UK where a surrogate has refused to give up the baby and all involved traditional surrogacy, conceiving with the surrogate's own egg," says Prosser.
"It happens rarely but it can be tricky if things aren't discussed in advance. In those cases, there would be no positive story to tell the child when it comes into the world. Ultimately, there are going to be easier ways for a surrogate to get pregnant."
So how do we increase the options? Raine-Fenning talks of advances in fertility treatments increasing options for older parents.
"Artificial wombs are here. We know babies survive for 24 weeks gestation in neo-natal intensive care. The distance between when you grow an embryo, freeze it and safely inseminate is growing ever longer."
But what of the commercialisation of the process in the US? Will we end up with a Handmaid's Tale Gilead, where the rich exploit the poor or a Hollywood demand for babies without the bump?
It's a bigger ethical issue. "We don't want these fertility treatments to be available to only those who can afford them," says Raine-Fenning. "We have to continue campaigning for equality and make sure people can access treatment irrespective of their financial situation."
What really cheers him, though, is the steady rise in egg and sperm donation after 2004, when a court ruling removed a donor's anonymity after their child turned 18.
"Donations dropped, then they doubled," he says. "It can't be stressed enough that without these people some families cannot have children of their own.
"It's Louise Joy Brown's 40th birthday this year - she was the first IVF baby. Think of how many babies have now been born with IVF. It's the same. The more we talk about surrogacy, the more acceptable it becomes."