HBO rings in the new year with “Angry Boys” (9 p.m.), a mock-documentary from Australia starring Chris Lilley as characters old and young, male and female. He plays Nathan and Daniel Sims, identical twins in a dusty rural town who curse and swear at each other almost all of the time. One is nearly deaf and the other is brutally insensitive to his condition. Lilley also plays “Gran,” a spunky 65-year-old guard at a juvenile detention facility where she dispenses tough love. Look for him as an American rapper, a Japanese wife and an aging Australian surfer.

Like many fake documentaries/acting showcases, “Angry” accentuates audacity, versatility and just plain weird silliness. It’s a little like being forced to watch a show-off at an improv group’s workshop. It’s impressive but not necessarily entertaining.

There are plenty of shows like this on other networks, forcing one to ask, “What’s this doing on HBO?” Or worse, “Why am I paying extra for HBO for the kind of quickie import I’ve already seen on IFC and BBC America?” This is not the way HBO should be responding when Showtime (“Homeland”), AMC (“The Killing”) and FX (“American Horror Story”) are getting better all the time.

• BBC America welcomes 2012 with a marathon of “Absolutely Fabulous” (6:20 a.m. to 5 a.m. Monday). This anticipates a 20th anniversary “Fabulous” special airing Jan. 8 on Logo and BBC America.

• Excess and indulgence of another sort unfold on “Drugs, Inc.” (7 p.m., National Geographic), a weekly look at America’s illegal narcotics underground.

• Not content with showcasing real critters, Animal Planet goes on a 10-episode snipe hunt with “Finding Bigfoot” (9 p.m.).

Tonight’s other highlights

• Discovery invites viewers to spend the day with a “Gold Rush” (9 a.m.) marathon.

• Scheduled on “60 Minutes” (6 p.m., CBS): An SAT cheater confesses; House Majority Leader Eric Cantor; Alex Honnold, a “freestyle” mountain climber.

• The Giants host the Cowboys on “Sunday Night Football” (7 p.m., NBC).

• On three episodes of “Once Upon a Time” (ABC): the price of gold (7 p.m.), a big decision (8 p.m.), memories return (9 p.m.).

• An illegal nanny faces scrutiny on “The Good Wife” (8 p.m., CBS).

• Julie Andrews hosts a New Year’s celebration from Vienna on “Great Performances” (8 p.m., PBS, check local listings).

• Brand-name chefs compete on “Rachael vs. Guy Celebrity Cook-Off” (8 p.m., Food).

• Vengeance consumes Cullen and Elam on “Hell on Wheels” (9 p.m., AMC). (This series has been renewed for a second season.)

• The 10th anniversary of 9/11 brings a time for reflection in Dearborn, Mich., on “All-American Muslim” (9 p.m., TLC).

Cult choice

A short, unpleasant Minneapolis musician pouts and speaks cryptically in the 1984 rock fantasy “Purple Rain” (7 p.m., VH1 Classic), starring Prince.