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A helicopter appeared in the sky over the North Sea.

It was 7 a.m. on a Wednesday this summer, and the helicopter circled in a wide arc before hovering above a ship traveling south at about 15 knots. At more than 1,300 feet long, the ship, the Mary Maersk, was hard to miss. It is longer than the Eiffel Tower is high, and the Mary and its sister ships are the biggest container ships in the world.

Feet appeared first from the helicopter, then a pair of Levis, and gradually a man was lowered by rope onto the ship’s deck. His job was to pilot the ship down a narrow dredged channel in the Weser River, toward the port of Bremerhaven, Germany.

As companies look for more efficient ways to move freight from factories in China to consumers in Europe, the Mary is among the newest giants known as the Triple-E’s. Owned and operated by A.P. Moeller-Maersk of Denmark, the world’s largest container-shipping company, the Triple-E’s went into service last year, muscling their way into the $210 billion container industry. They have also gained a following: Hobbyist spotters watch for the Triple-E’s and post pictures online, and Lego has created a mini version with 1,516 bricks.

Until the late 1990s, the largest container ships could carry about 5,000 steel shipping containers, each about 20 feet long. Today such ships are little more than chum. The size of container ships has exploded, reflecting their role as the packhorses of globalization. Each year, the maritime-shipping industry transports nearly $13 trillion worth of goods, roughly 70 percent of total freight, according to the World Trade Organization.

The Triple-E’s can carry more than 18,000 containers, piled 20 high, with 10 above deck and 10 below. But they can sail only between Europe and Asia, as their nearly 194-foot-wide hulls are too large to fit into U.S. ports or to slip through the Panama Canal.

The Mary will stop at a dozen ports, going from Gdansk in Poland to Ningbo, Yantian, and Shanghai in China. It carries seafood. It carries auto parts. It carries perfume, grated cheese and frozen pork. Computers and clothing are among China’s biggest exports, while chemicals and timber are more likely to leave Europe.

The Mary — stacked so high with cargo that little is visible beyond two smokestacks and a glassed-in command center — is an apt symbol for an increasingly global marketplace. But it also represents the container-shipping industry’s overreaching ambitions. Few carriers besides Maersk are profitable, too many new ships are being built, and demand for space on container ships is slowing as economies in Europe and Asia face head winds.

Maersk, based in Copenhagen, ordered 20 Triple-E’s from Daewoo of South Korea in 2011, increasing its worldwide capacity more than 10 percent. The timing was unusual. A report from the Boston Consulting Group, which counts Maersk as a client, called 2011 a year that “executives in the container-shipping industry would probably like to forget,” in part because a wave of new vessels ordered in earlier years swelled capacity.

But demand for space has lagged since 2008, according to Drewry, a shipping consultancy that tracks the industry. The idle space at Maersk amounts to one Triple-E.

“It’s a simple logic: Bigger is better — if you can fill it,” said Ulrik Sanders, global head of the shipping practice at Boston Consulting.

“There’s too much capacity in the market, and that drives down prices,” he continued. “From an industry perspective, it doesn’t make any sense. But from an individual company perspective, it makes a lot of sense. It’s a very tricky thing.”

“An arms race”

The captain wears Crocs. He is standing on the bridge, in black jeans and a white shirt with black stripes at the shoulders.

The captain, Franz Holmberg, is an easygoing Dane. He came from a farming family, but decided to try a life at sea and got hooked. After graduating from nautical school, he was a third officer on a ship that carried 3,800 containers, a fifth of Mary’s capacity.

“Every time a new series comes out, everyone says: ‘This is it; it can’t get any bigger,’ ” the captain says, adding, “Then a few years after, they just add a little bit more.”

The industry wants ships that carry more containers, more slowly. Fuel prices are a major factor, so ships now commonly “slow steam” to save fuel, cruising at 16 or 18 knots instead of 22. A typical trip from Poland to China takes 34 days.

During a recent voyage to the Suez, the Mary’s crew sailed on a parallel course with a 10-year-old Maersk container ship that held half as much cargo, but the Mary used only 6 percent more fuel.

“We’ve seen during the last 10, 15 years a dramatic increase in fuel costs,” said Jacob Pedersen, an analyst at Sydbank, a Danish bank. “That gives them reason to get rid of the old, uneconomic ships.”

But fuel is only one part of the equation.

“The supply of ships has far outstripped the growth rate” of container traffic, said Richard Meade, the editor of Lloyd’s List, a leading nautical newspaper. The top shipping lines, he added, “have entered into an arms race in terms of size, led by Maersk” and its Swiss rival, the privately held Mediterranean Shipping. Newer ships, he said, “are more efficient, more economically viable and more environmentally friendly, but they are only going to deliver those results if they are full.”

When the world economy slackens, so does the shipping industry. At one end of Mary’s route, the growth engine of China has been losing steam, while at the other, Europe is again flirting with recession.

The shipping industry has also lacked significant consolidation, with shipping giants often seen as national assets. The top five container lines are either family- or state-controlled. Revenue at Maersk, publicly traded but family controlled, equals more than 14 percent of Denmark’s gross domestic product.

Shipyards, conditioned to build ever-larger vessels, are cutting prices to keep their order books filled. The Triple-E’s were built for $190 million a ship, which in 2011 was seen as a relative bargain. By comparison, in 2007 China Shipping Container Lines, another major shipping line, paid about $170 million a ship — but those had a capacity of about 13,300 containers, nearly 5,000 fewer per ship.

“In this down cycle, the new-built prices are low and money is cheap, so you would much rather go and buy the vessels than go and acquire a company” that has older ships, said Martin Dixon, director of research products at Drewry. “Many shipping lines are struggling to make money, so cost leadership is key to survival. Hence, you’re seeing a lot of investment in bigger ships.”

The bigger ships, though, have been sustained by a growth rate in containerization traffic that has been 2½ to three times the global economic growth for decades — and that seems to be coming to an end.

“There are two types of companies that will survive this,” said Sanders, of Boston Consulting. “Either you have the very large companies like Maersk” that “take advantage of scale and make money, or particular shipping lines that operate a niche where they dominate, like a feeder line out in Southeast Asia.

“The other guys,” he said, “are caught in the middle and will have a hard time to make a decent return.”

While the ships grow, the crews don’t, in another economy of scale. The Mary has a multinational crew of 20 to 30.

The cost of the crew and a range of other expenses related to running the vessel account for more than a quarter of the Maersk Line division’s cost base. Fuel represents more than a fifth. Cutting such costs helps Maersk steady its results.

China’s huge footprint

Earlier this year, the Nicaraguan government announced plans to build a new canal system, bankrolled by a Chinese billionaire, that would compete with Panama and be wide enough to accommodate the Triple-E.

Such plans have been floated before and failed to materialize, but it is the kind of audacious project that only the Chinese might try. No country more than China has spurred the containerization boom, a byproduct of moving the world’s factories thousands of miles from their biggest markets.

Maersk is deeply embedded in China, with more than 20,000 employees there. It operates container terminals at seven Chinese ports, has bought 118 Chinese-made ships worth $3.5 billion and owns two Chinese factories that build containers.

China is also exerting its influence on the industry. The country’s regulators recently blocked an attempt by Maersk and two European rivals to form a partnership, saying it would hinder competition. Maersk recently proposed a less-ambitious alliance with a single rival, Mediterranean Shipping.

The proposed deals represent a concession that cargo volume is not rebounding as quickly, so shippers need to share costs and cargo space. Boats are typically full heading west to Europe and partly empty heading east to China. Cargo from Europe to Asia has grown about 30 percent in the past five years, in part because of rising demand from a growing Chinese middle class. But it has not nearly filled all the containers.

At the same time, some manufacturing is moving closer to local markets, a trend that contributes to slowing growth in container traffic. China, too, is trying to foster its own shipping lines. This year, China Shipping Container Lines ordered five ships that will each hold 19,000 containers, about 1,000 more than the Triple-E. They begin to arrive later this year.

How to park a whale

It was time to park the world’s largest container ship.

Several hours had passed since the first pilot arrived by helicopter, and a second, Karsten Burckner, 45, had come aboard from a tugboat gangplank. Soon he was on the far end of the ship’s bridge smoking cigarettes with the captain. He rolled the cigarettes by hand, while the captain preferred his Marlboros.

Burckner’s job was to help turn large boats in front of the harbor at Bremerhaven and back them into their spot alongside the port, where towering cranes would soon begin hoisting crates on and off the ships. Speedy, it is not.

Three tugboats nudged the Mary while the ship’s twin engines fired in opposite directions. The ship began a very slow 360. It eased toward large rubber cushions on the dock. Beyond were steel shipping crates, stacked like dominoes and stretching out in a vast paved expanse in the port. They were scooped up by gangly red vehicles called Straddle Carriers, which are not much wider than a truck but tall enough to carry three or four crates.

The two men looked over the ship’s side and spoke on walkie-talkies to sailors. Minutes passed — 10, 20, 30. The Mary, crawling at 0.1 knots, began sidling up to a pier.

“Compared to the whole size and the weight of the ship, the steel plates in the side are actually pretty thin,” the captain explained. “If we get a speed higher than that, we’ll start buckling plates.”

He smiled. “And that does not go well with anybody, obviously.”

Burckner, too, was once a container-ship captain — 11 years ago. But he had to give it up. “I was forced,” he said, pausing ominously and then smiling, “by my wife.” This is true of many pilots, who tend to be men who gave up the months at sea for home life.

His ship carried 2,500 containers. “That was a big container ship then,” Holmberg, the captain, explained.

“When I started, nobody was thinking that this size of vessel will be built,” Burckner said. “I don’t know where it will end,” he said, looking over its vast expanse. “Ask Maersk.”