On Shameless, William H. Macy plays the world’s most deadbeat dad.

Frank Gallagher is a boozy, shiftless grifter whose brood of six mix-and-match offspring (do any of them share the same mother?) care for one another and, by necessity, him.

“For all the craziness they go through, it is a tight-knit family, an honest family that loves each other fiercely,” says Macy. “That’s what the show is about.”

Airing Sunday at 9 p.m. on Showtime, Shameless began its third season recently with Frank coming to in Mexico, not sure how he got there and with no credentials to get himself home.

“I pride myself on taking the script and saying, ‘I can DO this!’” says Macy, clearly gleeful at the depths to which Frank routinely sinks. “I take all the stuff the writers can shovel my way!”

Well, almost.

“Once or twice I’ve said, ‘Too much. Too despicable,’ ” Macy admits. “But it’s the writers’ job to push that line, to put every character in really uncomfortable situations. So we have a good, healthy tug of war.”

The show barrels along a path that is heartbreaking and hilarious, while Frank sets the pace with his appalling level of substance abuse.

“I flatter myself that, as an actor, I do a pretty good drunk,” says Macy, who, while acknowledging he’s on the wagon right now, can draw on “a little firsthand experience.”

He is careful to modulate Frank’s drunken state.

“For a scene that takes place at 11 o’clock in the morning, well, that’s a four-beer buzz,” he explains, “as opposed to 11:30 at night, when Frank’s speech is very slurred.”

Wardrobe helps too; he wears the same clothes “almost all the time.”

Still, Macy isn’t the type to let vanity get in the way of a great performance. Although he has achieved offbeat leading-man status, a few years ago, he got the hankering to headline a TV series. By then his wife, Felicity Huffman, was flourishing on Desperate Housewives. Macy notes, “And she loved every part of it. I was jealous. “

So far, so good.

“I love Shameless so much!” he says. “You get big stuff to do in scenes that are tough to do, with volumes of dialogue and a character who talks fast. You have to know your part inside and out. It really tests you as an actor, every single week. And I’m a better actor for it.”