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He Yiran, 1, at home with his sister He Yueran, 12. He Yiran is the second child in the family. In wake of the approaching census, family's are having trouble registering their second child in the one-child state.Sean Gallagher

Li Yong'an and Elle Hong have a small surprise waiting for the enumerators who will soon visit their home to carry out China's once-a-decade census: the couple's three-year-old son.

It's hard to hide anything as rambunctious and outgoing as little Li Rui'an, but he's one of an unknown number of Chinese children who exist in person but not on paper.

Since Rui'an's birth in 2007, his parents have been trying to get their son the same official hukou household registration that their 16-year-old daughter has, which is required for Rui'an to attend public school. They've failed every time because Mr. Li - to Ms. Hong's consternation - refuses to pay the 180,000 yuan fine (nearly $28,000) for violating the country's controversial one-child policy.

Mr. Li, a chess coach who was fired from his job at Beijing Normal University for breaking the one-child rule, says he'll try again to register Rui'an when the census enumerators come to his door some time this month.

"I'll tell them honestly that this boy is an actual child," he said with a bitter laugh when asked how he'll answer the question of how many people live in the family's cozy 12th-floor apartment. "Right now, I guess there's only the three of us."

The number of Chinese families hiding extra children forbidden to them by harsh population-control policies is one of the many unknowns as the country conducts its most earnest and scientific effort yet to get a grasp on the real population of the world's biggest country. In an effort to persuade families to admit the real size of their families, the government has promised to collect reduced fines from families that reveal their "extra" children during the census period.

Many hope the census will rekindle debate within China's ruling Communist Party leadership about the merits of the 30-year-old population-control policy (which actually provides several loopholes to the one-child rule but nonetheless restricts the number of children most families can have).

As China's postwar baby-boom generation heads into their retirement years, often with one child to care for two parents, articles questioning the merits of continuing the population control policy have become regular features in the Chinese press, indicating at least some official tolerance of the exchange.

The country's National Population and Family Planning Commission estimates that without three decades of population-control measures, China's population - already a staggering 1.3 billion - would be 400 million higher.

While Mr. Li and others like him say that, for reasons of principle, they want to register their second children for the census without paying any fine at all, many other parents appear eager to take advantage of the semi-amnesty on offer. In the southern city of Guangzhou, an industrial hub that's a magnet for migrant workers from the poor countryside, police had to set up special processing centres to deal with the number of parents who came forward with unregistered children in the weeks before the Nov. 1 start of the census.

According to local media reports, some of those registered for the first time were already teenagers, hinting at the lengths some families have gone to in order to keep secret their decision to break the one-child rule. (The last census, in 2000, revealed a surprisingly low fertility rate of 1.22 in urban areas - lower than that in even neighbouring Japan - but demographers believe that figure was distorted by three million unreported births.) The government says part of the motivation for reducing the penalty is to get an accurate grasp of the number of children living among the tens of millions of migrant labourers who exist on the fringes of swelling cities such as Beijing, Guangzhou and Shanghai.

"We want to provide an education to these kids, but in many cases [with migrant workers]we don't know how many children there are. We need a better estimate of the number and distribution of these kids," said Duan Chengrong, director of the population studies centre at Beijing's Renmin University and one of those who helped design the census questions.

Prof. Duan estimated that as many as 4 per cent of elementary and middle school-aged children were not receiving any education at all - a huge number in a country the size of China. "That's a problem, not just for the children and their families, but also for the cities and the country."

Some of those with unregistered second children doubt that China will be able to get a completely accurate picture of their population so long as those who violate the population control policies face penalties of any kind.

"Do you think it's possible for the enumerators to knock on every door of every household?" asked He Kecheng, the owner of a small audio-visual supplies company in Beijing who with his wife has also refused to pay the fine for having a second child, their son Yiran, in early 2009.

Nonetheless, Mr. He said he would try again to register his son when the enumerators came.

Mr. He noted that President Hu Jintao and Premier Wen Jiabao have often said their goal is building a "harmonious society" in the country. Propaganda aimed at getting citizens to take part in the census carries the same message: "Carry out the census, build a harmonious society" reads one common banner on Beijing's streets.

"What is a harmonious society? For many Chinese, that means having a two-child family. It's that simple," Mr. He said.

Q & A with Yang Zhizhu who took a stand against China's one-child rule

Yang Zhizhu has become of a cause célèbre in China after he and his wife, Chen Hong, decided to break the country's one-child rule and to make a public stand in doing so.

The 43-year-old Mr. Yang was fired from his job as a law professor at Beijing Youth Politics College for refusing to pay a heavy fine for violating the population control policy after the couple's second daughter, Yang Ruonan, was born in December 2009.

Mr. Yang is understandably bitter about his situation, but he believes the demographic realities of China will soon force the government to abandon the controversial and unpopular law. He spoke to The Globe and Mail by telephone.

Q. Why did you decide to break China's population-control policies and have a second child?

A. I think this is a very odd question. If a person is born outside of the regulations, we should have them, killed? What kind of regulation is this?

Q. Have you managed to get your daughter registered yet?

A. It is impossible! They want me to pay a fine that is nine times the average disposable income in Beijing - 240,000 yuan (about $36,500). This is quite a lot!

Q. The government is promising lower fines to encourage people to report their second children for the census.

A. They are lying. They aren't charging less, they're charging us more, because the Family Planning Committee feels the once-child policy is almost certainly going to end (so they need to collect as much money as possible now). The census has no meaning at all. The government can simply add tens of millions of people to the result.

Q. Do you expect that the one-child policy is going to change after the census?

A. Maybe, but not because it. The data of census is false.

Q. So, you believe a change to the one-child policy is coming soon?

A. I think it might be, because after the economic crisis, the shortage of workers is getting worse. If they can't find people to do the work, then the government will be nervous.

Q. Have you been able to return to work?

A. No way. They don't allow me to work, but I'm still on the list of staff. This is working with Chinese characteristics. No work, no salary, and they ask money from me. This will last until the family planning policy is abolished.

Mark MacKinnon and Yu Mei