Some men are having vast numbers of children through sperm donation. This week the BBC reported on a man whose sperm contained a genetic mutation that dramatically raises the risk of cancer for some of his offspring.

One of the most striking aspects of the investigation was that the man’s sperm was sent to 14 countries and produced at least 197 children. The revelation was a rare insight into the scale of the sperm donor industry.

Sperm donation allows women to become mothers when it might not otherwise be possible – if their partner is infertile, they’re in a same-sex relationship, or parenting solo.

Filling that need has become big business. It is estimated the market in Europe will be worth more than £2bn by 2033, with Denmark a major exporter of sperm.

So why are some sperm donors fathering so many children, what made Danish or so-called “Viking sperm” so popular, and does the industry need to be reined in?

If you’re a man reading this, we are sorry to break it to you, but the quality of your sperm probably isn’t good enough to become a donor – fewer than five in 100 volunteers actually make the grade.

First, you have to produce enough sperm in a sample – that’s your sperm count – then pass checks on how well they swim – their motility – and on their shape or morphology.

Sperm is also checked to ensure it can survive being frozen and stored at a sperm bank.

You could be perfectly fertile, have six children, and still not be suitable.

Rules vary across the world, but in the UK you also have to be relatively young – aged 18-45; be free of infections like HIV and gonorrhoea, and not be a carrier of mutations that can cause genetic conditions like cystic fibrosis, spinal muscular atrophy and sickle cell disease.

Overall, it means the pool of people that finally become sperm donors is small. In the UK, half the sperm ends up being imported.

But biology means a small number of donors can make vast numbers of children. It takes just one sperm to fertilise an egg, but there are tens of millions of sperm in each ejaculation.

Men will come to the clinic once or twice a week while they’re donating, which can be for months at a time.

Sarah Norcross, the director of the Progress Educational Trust charity which works on fertility and genomics, said the donor sperm shortage made it “a precious commodity” and “sperm banks and fertility clinics are maximising the use of available donors to meet demand”.

From this small pool of donors, some men’s sperm is just more popular than others.

Donors are not chosen at random. It’s a similar process to the savage reality of dating apps, when some men get way more matches than others.

Depending on the sperm bank, you can browse photos, listen to their voice, find out what job they do – engineer or artist? – and check out their height, weight and more.

“You know if they’re called Sven and they’ve got blonde hair, and they’re 6 ft 4 (1.93m) and they’re an athlete, and they play the fiddle and speak seven languages – you know that’s far more attractive than a donor that looks like me,” says male fertility expert Prof Allan Pacey, pictured, who used to run a sperm bank in Sheffield.

“Ultimately, people are swiping left and swiping right when it comes to donor matching.”

Denmark is home to some of the world’s biggest sperm banks, and has gained a reputation for producing “Viking babies”.

Ole Schou, the 71-year-old founder of the Cryos International sperm bank where a single 0.5ml vial of sperm costs from €100 (£88) to more than €1000 (£880), says the culture around sperm donation in Denmark is very different to other countries.

“The population is like one big family,” he says, “there is less taboo about these issues, and we are an altruistic population, many sperm donors also donate blood.”

And that, Schou says, has allowed the country to become “one of the few exporters of sperm”.

But he argues Danish sperm is also popular due to genetics. He told the BBC the Danish “blue-eyed and blonde-haired genes” are recessive traits, which means they need to come from both parents in order to appear in a child.

As a result, the mother’s traits, such as dark hair, “might be dominant in the resulting child”, Schou explains.

He says demand for donor sperm is coming mainly from “single, highly-educated, women in their 30s”. They now make up 60% of requests.

One aspect of the sperm donor investigation published earlier this week was how a man’s sperm was collected at the European Sperm Bank in Denmark and then sent to 67 fertility clinics across 14 countries.

Nations have their own rules on how many times one man’s sperm can be used. Sometimes it is linked to a total number of children, others limit it to a certain number of mothers (so each family can have as many related children as they want).

The original argument around those limits was to avoid half-siblings – who didn’t know they were related – meeting each other, forming relationships and having children.

But there’s nothing to stop the same donor’s sperm being used in Italy and Spain and then the Netherlands and Belgium, as long as the rules are being followed in each country.

This creates circumstances where a sperm donor can legally father large numbers of children. Although the man is often in the dark about that fact.

“Many recipients, and also donors, are unaware that a single donor’s sperm can be lawfully used in many different countries – this fact should be better explained,” says Sarah Norcross, who argues it would be “sensible” to bring down the number of children one donor can have.

In response to the investigation into the sperm donor who passed on a gene that led to cancer in some of the 197 children he fathered, officials in Belgium have called on the European Commission to establish a Europe-wide sperm donor register to monitor sperm travelling across borders.

Deputy prime minister Frank Vandenbroucke said the industry was like the “Wild West” and “the initial mission of offering people the possibility of a family has given way to a veritable fertility business”.

The European Society of Human Reproduction and Embryology has also proposed a limit of 50 families per donor across the EU. That system would still allow one donor’s sperm to make more than 100 children if the families wanted two or more babies each.

Concerns have been raised about the impact on the children conceived through sperm donation. Some will be happy, others can be profoundly distressed by the double discovery of being made with donor sperm and being one of hundreds of half-siblings.

The same is true of donors, who often have no idea their sperm is being so widely distributed.

These risks are amplified by readily available DNA ancestry tests and social media where people can search for their children, siblings or the donor. In the UK, there is no longer anonymity for sperm donors and there is an official process through which children learn the identity of their biological father.

Mr Schou at Cryos argues more restrictions on sperm donation would just lead families to “turn to the private, totally unregulated, market”.

Dr John Appleby, a medical ethicist at Lancaster University, said the implications of using sperm so widely was a “vast” ethical minefield.

He said there are issues around identity, privacy, consent, dignity and more – making it a “balancing act” between competing needs.

Dr Appleby said the fertility industry had a “responsibility to get a handle on the number of times a donor is used”, but agreeing global regulations would be undeniably “very difficult”.

He added that a global sperm donor register, which has been suggested, came with its own “ethical and legal challenges”.