The city’s runaway and homeless children are breaking the bank, according to a report released yesterday.

Fueled by more discretionary funds from the City Council, Mayor Bloomberg’s spending on services for underage runaways and homeless New Yorkers more than doubled to $12.8 million in the current fiscal year, compared to $5.3 million in FY2005, according to the study by the Independent Budget Office.

The city’s increase comes as federal and state contributions have dipped, IBO said.