This tiny island is so jam-packed that even the dead have begun fighting for space.

Living in Hong Kong is a constant battle for elbow room, with 5 million people crammed into an area about half the size of Washington. The poor live like boxed matchsticks, the middle class not much better, and the rich need expense accounts to afford monthly rents of $6,000 for a three-bedroom apartment.

Lately, the space crunch has begun following everyone right to the grave. A permanent tomb in a private cemetery now runs $25,000--if you can find one. The old wheeze about people dying to get in has never been truer, but there are few vacancies, even for millionaires.

Two public burial places are accepting coffins for short stays only. There is something called "exhumation cycle," which requires that the dead be dug up after six years to make way for the next generation. The burial fee is just $40, but the exhumation levy is $350.

The Hong Kong government, which maintains strict control over land use, refuses to apportion more territory to the dead. Rather, it actively encourages cremations by offering to do the job for as little as $20.

But the idea of reducing loved ones to ash still rankles Hong Kong's traditional Chinese, who consider ancestral worship a cardinal tenet of Confucianism.

So the good governors of this British colony are making it possible to burn relatives and bury them too. All over the island, high-rise structures called columbaria, which in essence are tenements for the dead, are being built to store ashes in 9-by-9 inch vaults that can be visited like graves.

"We are trying to convince people that paying respect to ashes is just as good as paying respect to a grave," explained Lai Chukong, staff officer for Hong Kong's cemeteries and crematoria.

Columbaria really are multistory walls subdivided by the vaults that are inserted like safe-deposit boxes at a bank. The vaults, or "niches" as they are called, are covered by a commemorative plaque bearing a picture of the deceased, his name and date of death.

An individual niche now costs $150, while a family-sized vault big enough for the ashy deposits of four goes for about twice as much.

Niches implanted high on the columbarium can only be reached by climbing several flights of stairs and walking down a long ramp. One new, 10-story structure has room for the remains of 20,000.

For Hong Kong residents who insist on a linear cemetery but cannot afford the price, there is an earthier alternative. A few private graveyards have developed "urn cemeteries" offering tiny plots for permanent burial of ashes or bones with just enough space for a small gravestone.

But land for urn burial has nearly been exhausted and may soon face new regulations requiring six-year burial rotation.

Then there is the China option. Anxious for foreign exchange, Communist authorities have agreed to inter Hong Kong's dead in a dusty border town about an hour's train ride away. The price is $2,500, to be paid in Hong Kong currency.

But logistical problems have kept all but 95 coffins from crossing the border in the past three years. Transportation is the main obstacle, there being no direct route to the Chinese boneyard. Travel to China also presents trouble because of the complicated visa procedures.

Despite these hangups, China may provide the best long-run solution for disposing of Hong Kong's dead aside from cremation, according to officials here.

Before the Communists took control of China in 1949 and banned use of productive land for graves, thousands of overseas dead, Chinese businessmen from Southeast Asia and railway workers from America, were sent back every year for burial in their "old home."

The bodies stopped first at a Hong Kong institution called Coffin House, which stored the pine boxes until they were ready for shipping to the mainland. The place became known to overseas Chinese worldwide as "Hotel for the Dead."

Coffin House, which is run by a Hong Kong hospital, still functions today in a reduced capacity. It collects the few caskets destined for the new Chinese burial ground across the border. Other urns, caskets and boxes of bones awaiting burial in Hong Kong sit in storage there.