That cheese grater, bookcase and those cute patterned pillows that you just picked up at IKEA surely must have made their way to the Sunrise store via a South Florida port.

Guess again. IKEA’s massive distribution center that serves its stores from North Carolina to Texas and on down the Florida peninsula is located just outside the port of Savannah. So are the 1.4 million-square-foot International Home Depot Distribution Center and the distribution hubs for a who’s who of big box stores.

Despite having 15 seaports, about 45 percent of the containerized cargo consumed in Florida arrives via ports in other states, according to a trade and logistics study commissioned by the Florida Chamber of Commerce Foundation.

When it comes to Asian imports consumed in Florida, just 38 percent entered via one of the state’s seaports. Sixty-two percent of those imports arrived in other ports: 36 percent came to Los Angeles/Long Beach and were trucked across the country or moved by rail, 13 percent came in through Savannah and 4 percent arrived in the Port of New York and New Jersey, according to the 2010 Florida Trade and Logistics Study.

All told, 11 million tons of imports used by Floridians entered the United States through other states’ ports.

And that’s a problem for PortMiami Director Bill Johnson. “We need to win back a large chunk of Asian trade for Florida,’’ he said. “For the last 10 to 15 years, Florida has been asleep.’’

Johnson, who is also chairman of the Florida Ports Council, the association for the state’s 15 deepwater seaports, said because of the competition posed by other East Coast ports, Florida ports can’t act like “little bickering children fighting over crumbs on the table.’’

The state’s ports, he said, need to present a united front to make Florida the preeminent state for international trade in the next five years.

While Florida ports compete among themselves for cargo, he said, now they have a common agenda when they go to Tallahassee and Washington.

“I’m not trying to undercut [the other Florida ports]; I’m trying to raise my bar,’’ Johnson said.

“There’s no reason Orlando shouldn’t be served by a Florida port. After the dredge, that cargo should shift back to Florida — primarily Miami,” said Kevin Lynskey, Miami’s assistant port director for business initiatives. The rest of the equation for PortMiami is to lock in South Florida cargo and pick up a small percentage of containers headed for Atlanta and other points north, he said.

“Florida faces a once-in-a-generation opportunity to fundamentally transform its economy. The shift in U.S. population growth to the south, the Panama Canal widening, the resurgence of Latin America and the Caribbean trade, and the continued revolution in logistics practices create the opportunity for Florida to become a global trade and logistics hub,’’ said the chamber study.

Among the study’s recommendations: Have at least one Florida seaport dredged to 50 feet with an on-dock or nearby rail connection by 2014.

That would be Miami, which should have its harbor deepening project completed while some ports are still studying the feasibility of dredging.

The port has already begun a project to strengthen its wharves and rebuild the seawall in anticipation of the “deep dredge.” Contracts for the dredge itself are expected to be awarded in February and the target date for completion is the summer of 2015. The main channel, which extends 2.5 miles out to the sea, will be dredged to a depth of 52 feet, and the port’s south channel, which faces Fisher Island, will be readied to a depth of 50 feet.