But Catholics who want to celebrate Mass without restrictions, or talk freely about the conclave in Vatican City that will choose the next pope, are better off going someplace else.
That's because the bishop of Beijing, Fu Tieshan, answers not to the Vatican, as do bishops in the rest of the world, but to the Communist Party's state-run church. Even other state-appointed bishops who have been quietly recognized by the pope must remain publicly loyal to Beijing above the Vatican.
This tug of loyalties frames the question that will face the next pope in choosing how to engage with China and its estimated 12 million Catholics: To forge a deeper connection with the faithful, should he work to establish deeper ties with Beijing even at the cost of acquiescing to the party's control of the church?
In exchange for a closer relationship with Catholics in China, the next pope may have to accept that its bishops here will not be outspoken on issues of importance to the Vatican, and may in fact alienate many underground Catholics, who number in the millions.
"The question is always what kind of price, what kind of compromises the Vatican is willing to make with regard to the appointment of bishops," said Richard Madsen, author of the book China's Catholics. "If it should bend a little more than the present pope did, I think this would upset the present underground."
Likewise, Beijing could claim a diplomatic success by establishing formal relations with the Vatican. But that also could increase the influence here of the next pope, with full knowledge that Pope John Paul II helped end communism in Eastern Europe.
The next pope may be in no hurry to resolve the China question, which has grown increasingly complex in the past half-century, since Mao Tse-tung established the Chinese church bureaucracy and the Vatican recognized Taiwan.
"For the new pope, probably he will slow down the process, because you know, for Pope John Paul II the Sino-Vatican relationship was an urgent thing. He knew that he had limited time," said Anthony Lam, senior researcher at the Holy Spirit Study Centre in Hong Kong. "But for the new pope, the Sino-Vatican relationship is important but not urgent."
After years of systematic repression of Catholics, including the destruction of churches and persecution of priests during the Cultural Revolution under Mao, the central government's virulent antagonism toward organized religion has in most cases become a more pragmatic wariness.
Today, party leaders still fear the potential threat that popular religious and spiritual followings could pose to the party. They still seek to discredit some of these movements as "evil cults," such as Falun Gong. But officials view Catholicism and other mainstream religions as forces to be co-opted and controlled.
It means that in some areas non-state-church Catholics still live in fear of discovery, harassment and arrest. They tend to worship in private homes, with the locations and times of Mass changing from week to week. They have observed this pattern in mourning the pope's death.
"They are not allowed to do that, but they are still doing it secretly in people's homes, in the fields, and just any place they can do it secretly," said Joseph Kung of the Connecticut-based Cardinal Kung Foundation, an advocacy group for dissident Catholics in China. "And if they are caught, if they are found doing these kinds of prayers, I'm afraid the government is not very lenient about it."
In the days before the pope's death, two bishops, two priests and a layman were arrested, several of them in the province surrounding Beijing, Hebei, a center of underground Catholicism, according to the Vatican and Catholic groups.
Authorities in some provinces have a long history of detaining underground bishops and priests: Gao Kexian, a bishop in the coastal province of Shandong south of Beijing, died in January after more than five years in custody; the whereabouts of a Hebei bishop, Su Zhimin, who was arrested in 1997, are unknown.
But in many regions, underground Catholics can practice with relative freedom, sometimes in tacit alliance with official state church bishops, who in turn have quietly been recognized by the Vatican.
The Vatican has hoped that the underground and official churches in each diocese could settle on bishops acceptable to both.
In some places where this has happened, the official church has absorbed the underground followers.
In a pragmatic sense, this blurring of the lines pays off for both the Vatican and the Chinese government. The Vatican becomes more connected to the lives of millions of Chinese Catholics as it quietly recognizes official bishops, and the Chinese government undermines the position of the underground by allowing a closer relationship between its bishops and the Vatican.
But each side pays a price also. Some underground Catholics have felt abandoned as they noted greater cooperation between the Vatican and the Chinese government. And the Vatican finds itself with bishops who would not dare openly question official state policies.
A Catholic priest in Beijing said this may be "the best deal available now so that we can continue to deliver the message to our people."
"The over-ground [Catholic] position is a say-nothing, do-nothing, let's live quiet lives," said the priest, who spoke on condition of anonymity. "They rattle the cages and say, 'Look how brave we are,' but even if the cage was opened they wouldn't walk out."
Meanwhile China risks seeing its official bureaucracy - the Chinese Catholics Patriotic Association set up in 1957 - peopled with bishops and priests who are privately more sympathetic to the Vatican than to their superiors in Beijing.
Pope John Paul appeared close in 1999 to establishing diplomatic ties with China, which necessarily meant ending relations with Taiwan, the self-governing island that China views as a renegade province. But the pope was apparently unwilling to surrender final say over the appointment of bishops, which Beijing insisted upon.
Shortly after that, Beijing appointed several bishops without consulting the Vatican. In 2000, the pope angered Beijing by canonizing 120 missionaries and Chinese believers who had been killed in China. Then, in 2001, the pope apologized for past wrongs committed by Catholics against China.
The pope's death may have exacerbated the tensions. China offered its condolences, and state media reports in the days after his death were fairly extensive.
But for the past week propaganda officials have sharply curtailed state media coverage as well as Internet chat about the pontiff. That is likely related to the decision by the Vatican to receive Taiwanese President Chen Shui-bian for the pope's funeral, which prompted protests from Beijing.