“There are many women who won’t get married, so they might not fulfil this fundamental biological mission,” Xiaogunzhu said, using the name she blogs under to avoid any negative attention, “but I felt another path had opened up”.

Her baby, now nine months old, is called Oscar after a character in a comic about the French Revolution – a nod to the donor’s French ancestry.

Many feel that struggling to find, or not wanting, a partner should not preclude them from motherhood.

Xiaogunzhu believes a father isn’t necessary – her own was controlling and often angry, dimming her view of the traditional family set-up. “Why does everyone think that children will ask: ‘Why don’t I have a father?’” she said.

Analysts predict that the total market in China for fertility services will reach US$1.5 billion in 2022 – more than double its 2016 value. Demand for services overseas for Chinese nationals is also booming.

Danish sperm and egg bank Cryos International has created a Chinese website and added Chinese-speaking staff. American and European sperm banks say that they have increasing numbers of Chinese clients. But the journey is neither cheap nor easy.

China’s national health department stipulates that the purpose of sperm banks is for “treating infertility and preventing genetic diseases”. In practice, that prohibits unmarried women from using them.

The cost of conceiving a child through a foreign sperm bank starts at 200,000 yuan (US$28,500). Women must make several trips abroad for the medical procedures, as Chinese law bans importing human sperm. Women also face discrimination; in Chinese culture, marriage is still considered essential to having a child.

Zhang has written more than 60 letters to delegates of China’s parliamentary body asking them to overturn the restriction as part of her work with Diversity Family, the NGO she co-founded to advocate for non-traditional family structures. “The state does not do this, so the people can only find their own way,” said Zhang.

In China, sperm donors must remain anonymous. But international sperm banks offer women details like hair colour, childhood photos and ethnic background.

“If you choose to use a sperm donor, sperm is essentially a commodity,” said Carrie, a 35-year-old single mother living in southwest China who also requested anonymity. Carrie said that international sperm banks are more sophisticated than Chinese ones, and “able to meet consumer demand”.

Peter Reeslev, the chief executive of Cryos International, said that given the extra choices, “Chinese women tend to choose Caucasian donors”. Reeslev said one possible reason is that sperm banks outside China have fewer Chinese donors – Cryos has only nine donors out of 900 who identify as Chinese.

US sperm bank California Cryobank has 70 available donors out of 500 who identify as Chinese. But experts say regardless of the availability of Chinese or Chinese-American donors, women are still choosing to have mixed-race children.

“Basically, the selected sperm donors are mostly white,” said Xi Hao, a clinical coordinator in Beijing who helps Chinese customers access a fertility clinic in California.

Zhan Yingying, a co-founder of the Diversity Family organisation, said it was rare for her to come across a mother who chose a sperm donor of Chinese ethnicity. Traits such as double eyelids and pale skin are often valued according to Chinese beauty standards.

“Before choosing the sperm donor I had not considered a particular race,” insisted Carrie, but after seeing the catalogue she realised she had a preference for foreign physical traits – and now has two half-Danish children.

For baby Oscar, Xiaogunzhu said personality was the major factor in her decision, as the donor was listed as “full of joy”.

But on her Weibo blog, photos of Oscar with the hashtag #mixed-race baby draw admiration.

“I personally don’t care about the colour of the skin,” she said. “I only care that the eyes are big and the features are good.”