The Brokeback Mountain co-stars, who became parents to MATILDA last month (NOV05), have been sharing the home since Ledger moved over to the Big Apple from Los Angeles.
But their low-key existence is no more, after their address was unveiled.
Williams says, "I'd been living (in Brooklyn) for a while, but Heath fell for it as soon as he spent time there.
"We had lived in blissful anonymity. Then the story came out, and there were photographers around the next day.
"I'm deeply shy, and I don't like anybody looking at me."
Lindsay Lohan really did write down her now infamous list of lovers, which has been providing gossip fodder for a couple of weeks now. But...