A Brooklyn dad with more than 70 previous busts was freed without bail Monday after allegedly leaving three young kids alone at home, where a fire broke out and trapped and seriously injured them.

Anthony Halliburton, 37, was released from custody shortly after his arraignment in Brooklyn Criminal Court on three counts each of child abandonment and endangering the welfare of a child involving Sunday’s horrific 11 a.m. blaze.

Halliburton — whose alleged child-related crimes aren’t eligible for bail under the state’s controversial criminal-justice reforms — had been arrested in the past mainly for the unauthorized sale of fare cards and forged tokens, law-enforcement sources told The Post.

Two of his prior arrests also were for drug possession, sources said.

All but two of his dozens of arrests occurred in the Bronx, sources said. One of the drug busts was in Manhattan, while a token arrest occurred in Brooklyn, sources said.

The injured children — a 4-year-old boy, 5-year-old girl and 8-year-old girl — were hospitalized Sunday after fire torched the family’s 11th-floor apartment on Livonia Avenue near Sackman Street in Brownsville, according to FDNY officials and court papers.

Halliburton is the biological father of the two younger kids and the stepfather of the 8-year-old, court documents say.

Firefighters raced into the building, broke into the apartment and grabbed all three kiddies within 12 minutes of receiving the call, said John Hodgens, chief of department for the FDNY, at a Sunday press briefing.

The door to the apartment was locked when the city’s Bravest arrived.

After they busted in, they found two of the kids in the living room and one laying right behind the front door, Hodgens said.

All of the children were found unconcious, officials said.

“It’s amazing that they were able to get up there and do that,” Hodgens said of the firemen.

An 11^th floor neighbor who was home during the blaze said she didn’t hear fire alarms blaring – but a loud banging caught her attention.

“I didn’t smell anything, I was on the other side of the hallway,” said the neighbor, a 19-year-old named Aniah. “Then I heard, like, banging … I thought it was a couple arguing but they weren’t.”

When she opened her door, she was greeted with a flood of smoke that had spilled into the hallway.

She said she wanted to get out but that firefighters told her to stay put.

Other neighbors reported hearing similar banging, with one woman saying she thought someone was hammering on her window.

“So I opened it, and I saw everybody looking up,” she said. “I came out, and I looked up, and I saw the fire and the smoke coming out through the windows. … It was big, black smoke covering the whole sky.”

It’s still not clear why the fire started. The dad told cops he was out getting groceries at the time, court papers show.

There were no previous domestic calls to the home, sources said.

Neighbors only spoke about the children’s mother, telling The Post she was a good person who always watched her kids.

“I saw [her] … playing with her babies in the hall,” said a female neighbor who did not want to be identified.

“She’s such a nice girl,” the woman continued. “She’s only lived here for a year now. … It’s so sad.”

Another neighbor who also did not want to give their name said he often sees the mom in the building with her three kids in tow.

“She’s a good lady,” he said. “She be with her kids all the time.”

-Additional reporting by Haley Brown and Kevin Sheehan