NEW ORLEANS — Five years after Hurricane Katrina destroyed more than 200,000 Louisiana homes, the state program established to help families rebuild still hasn’t paid out more than three-quarters of a billion dollars and has come under fire from a federal judge for discriminating against black homeowners.

The Road Home program, which state officials developed in July 2006 to funnel grants of up to $150,000 to Louisianans whose homes were destroyed or damaged by huricanes Katrina and Rita in August and September 2005, has disbursed about $8.6 billion to about 127,000 families.

But officials of the Louisiana Office of Community Development acknowledged this week that more than $777 million remained in the fund as the fifth anniversaries of the devastating storms approach. That money should be going in direct payouts to about 3,000 eligible families and to help cover other recovery costs.

The unallocated Road Home funds have sat around for so long that they’ve outlived the state agency that initially ran the program. Road Home is on its second parent after the Community Development Office’s Disaster Recovery Unit assumed oversight when the Louisiana Recovery Authority — which oversaw rebuilding from the hurricanes — went out of business at the end of June, as planned by legislators in the wake of the storms.

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