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An antitrust suit against Zillow over how it displays real estate listings could cripple the platform, the company said in court filings Friday, warning that the case may ruin the nation’s most popular website to search for homes for sale.

Real estate startup REX has asked a federal court to force Zillow and its subsidiary Trulia to stop separating homes for sale into two groups — those listed by brokers who belong to the National Association of Realtors and those listed by others. But contractual restrictions require Zillow to segregate the listings, the company said.