The rush to beat Jan. 1’s capital gains tax hike has resulted in an unprecedented leap in real-estate closings, including three Manhattan development sites.

Homebuilder Toll Brothers bought one ready-to-build site at First Avenue and 52nd Street — and another in Soho that will wait for the city’s residential rezoning.

At the same time, Bobby Cayre’s Aurora Capital Associates and the Adjmi family purchased a stalled site in Harlem and will start construction on Feb. 1.

The 130,000-square-foot stalled but ready-to-build site at 5-15 W. 125th St. was purchased from RGC Longview in an off-market transaction for $15.5 million, or about $120 per buildable square foot.

In the Soho/Hudson Square area, Toll Brothers paid $56.5 million to the longtime family owners of a two-story 40,000-square-foot garage building at 78-86 King St. that has an additional 160,000 square feet of air rights.

Toll Brothers paid $64 million for 953-961 First Ave.