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Macy is proud to be the drunken dad in ‘Shameless’

William H. Macy plays an alcoholic on the Showtime series “Shameless.”

Scott Gries/Invision via AP

William H. Macy plays an alcoholic on the Showtime series “Shameless.”

NEW YORK — On ‘‘Shameless,’’ William H. Macy plays the world’s most deadbeat dad.

He stars as Frank Gallagher, 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. The oldest daughter, Fiona (played by Emmy Rossum), is the family’s de facto mom, a Wendy to Frank’s derelict Peter Pan.

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‘‘Derelict’’ is putting it mildly. Frank is abrasive, self-absorbed, scheming, and delusional, a pickled patriarch whose most dignified moments find him passed out on the bathroom floor of the family’s ragtag South Chicago digs, or on a random street corner or maybe public park.

But somehow the family stays afloat, even with Frank dragging everybody down.

‘‘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 funds or credentials to get himself home.

Ever the schemer, he figures out a way. Just as, this week, he figures out a way to score some drinking money: He volunteers to take a neighbor’s infant to the doctor for a scheduled vaccination, then spends the cash meant for the doctor at his favorite bar. He pricks the baby with a thumb tack to simulate a shot, and shares a few drops of his whisky to calm the baby’s crying.

‘‘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. It’s over the line,’ ’’ Macy admits with a laugh. ‘‘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 both heartbreaking and hilarious, while Frank sets the pace with his appalling level of substance abuse. But the series doesn’t glorify drinking, however riotously drinking is depicted.

‘‘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 as the day wears on.

‘‘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.’’

Playing a drunk, which Macy deems less a thespian technique than ‘‘a parlor trick,’’ comes with pitfalls: A great impersonation of a drunk can distract an actor from the primary substance of the scene.

‘‘But if I’m pretty clear what the scene is about, then I just add on the drunkenness — slurring or stumbling — and it takes care of itself.’’

Although he has achieved offbeat leading-man status in such films as ‘‘Fargo’’ (for which he landed an Oscar nomination) and the made-for-TV ‘‘Door to Door’’ (which he also co-wrote), the 62-year-old Macy has had a busy career on screen and on stage as a celebrated character actor.

But 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. I said, ‘I want to do TV, too!’ ’’

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. I wish I’d done this earlier in my career.’’

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