Alec Baldwin is now a defendant in a wrongful death lawsuit filed by the family of Halyna Hutchins.

In the lawsuit, lawyers for the family list what they say are the lapses in safety on the "Rust" set ... lapses they claim led to the cinematographer's death.

Among the alleged lapses ... live ammo on the movie set. The suit also claims other shortcomings ... the crew failed to treat the gun as if it were loaded.

As for Baldwin, the suit claims he was only 4 feet from members of the crew and reached across his body and used his right hand to grab the revolver holstered on his left side, drew the revolver with a cross draw movement and aimed it directly at Hutchins while drawing back the hammer.

The suit claims, "He released the revolver's hammer, and -- BAM -- defendant Baldwin fired the revolver." Baldwin said in an interview he did not pull the trigger, but at a news conference Tuesday the Hutchins' lawyer said "I think it's clear what happened. Alec had the gun in his hand, he shot it -- Halyna was killed. The gun cannot fire unless the trigger is engaged and the hammer is back."

The suit says Baldwin never checked the gun himself for ammo before using it.

The suit also talks about cost-cutting measures and, a few days before Hutchins' death, a local camera operator made safety complaints to the producers that there had been 3 unsafe weapons discharges and the set was "super unsafe."

The unit production manager responded "with callous sarcasm," according to the lawsuit, saying the accidental discharges were "awesome" and "sound[ed] good."

Among the cost-cutting measures ... the hiring of inexperienced armorers, requiring the armorer to split time as an assistant props master, establishing and aggressively adhering to unreasonably rushed production schedules.

In addition to Baldwin, the armorer, Hannah Gutierrez-Reed and the assistant director, David Halls, are being sued, among many others ... including various production companies. The company that provided the ammunition is also a defendant.

The suit, filed by Hutchins' husband and son, asks for unspecified damages, including punitive damages. They're repped by L.A.-based Panish, Shea, Boyle, Ravipudi LLP.

While Baldwin himself has denied culpability -- pointing the finger elsewhere -- Hutchins' family had been slow to indicate who they think is actually responsible, until now.

Others have been much more willing to assign blame early in the process ... including a "Rust" gaffer, Serge Svetnoy, who sued AB, the armorer and others for what he called a reckless and negligent display of movie-making.

As you know, there have been different accounts of what exactly went down. Everyone agrees they were in the middle of setting up a shot, with Halyna and director Joel Souza framing up Alec for what was going to be a scene featuring the gun.

Svetnoy claims Alec had no business aiming the gun at Halyna and Joel -- but Alec himself argues differently, saying he was simply following their instructions ... and didn't even pull the trigger. He says when he let go of the cocked hammer ... the pistol fired unexpectedly.

He also says he never knew there was live ammo in the chamber, which has become a huge issue for investigators -- namely, how the hell did real bullets make it onto the film set???

Baldwin's hinted he feels head armorer Hannah Gutierrez-Reed and assistant director Dave Halls should bear responsibility for the fatal accident. Meanwhile, Hannah's pointed the finger in Alec's direction, claiming he didn't respond to her request for him to take safety lessons ... and she allegedly wasn't informed the star would be handling a gun on that fateful day.

Not to be forgotten ... there's a looming criminal investigation off in the distance that's still underway in New Mexico, where authorities have yet to exclude anyone, including Baldwin, of potential charges as they continue to look into what exactly happened.

As all of that has been playing out ... Halyna's loved ones have been grieving.

She leaves behind a husband, Matt, and a young son. She was just 42.