Agents. Can’t live with ’em, can’t live without ’em — especially when they’re named Ari Goldberg and, as played by actor Jeremy Piven, are the most compelling reason to tune into “Entourage,” the hit HBO series that returns to the screen Sunday night.

As you may recall, last August, Ari (Jeremy Piven) was finally axed by hotshot young actor Vincent Chase (Adrian Grenier). This came about after Ari, succumbing to the adrenaline and arrogance that are to his career what wheels and gasoline are to a Ferrari, needlessly insulted a senescent but legendary Hollywood producer, thereby losing Vince the lead role in “I Wanna Be Sedated,” a biopic about the legendary punk band the Ramones in which Vince was desperate to star.

After flirting with two mega-agencies, each of which staged a pompous presentation promising to turn Vince into a global brand on the level of Coca-Cola and Apple, Vince and his entourage (dictionary definition: “attendant persons”) decided they were ready to forgive Ari, provided he was willing to look them in the eye and apologize for being such a jerk. After all, they reasoned, Ari may be an obscene, completely untrustworthy snake of a human being, but at least he’s a human being. In Hollywood, that’s saying quite a lot.

Alas, Ari misread the cues and instead of simply saying “sorry,” he had his agency stage a pompous presentation promising to turn Vincent Chase into a global brand on the level of … Microsoft and McDonald’s. Vince and his buddies walked. End of Ari.

Well, not really. Not that it’s news, but “Entourage” needs Ari. It also needs Lloyd (Rex Lee), Ari’s gay, much abused, Chinese-American assistant, along with Ari’s regal, Pilates-slender wife (Perrey Reeves), who is one of the understated delights of the series. Luckily for us, all three are still around. Nonetheless, the second half of Season 3 (no, this is not a “new” season, but the continuation of last season) revolves around Vince’s gorgeous new agent, Amanda (Carla Gugino), and the curious dilemma that arises when Vince and his manager, Eric (Kevin Connolly), realize that, because Amanda is beautiful, classy, and female, they can’t say no to her even when they’re uninterested in a project she’s trying to foist on them.

Another dictionary definition of “entourage” is “surroundings,” and one of the show’s curiosities is that its peripheral figures are often more compelling than the four rock-solid homeboys at its core. As the lead, pretty-boy Vince is in some ways the least interesting character, while at the same time being completely convincing. Vince is a cipher, a good vibe on legs who illustrates something that Michael Tolkin, author of that other masterpiece of Hollywood inside-dopesterism, “The Player,” once told me — namely that, contrary to popular perception, the shrewdest people in Hollywood are not the directors and writers and studio heads, but the mega-wattage actors conventionally regarded as dummies.

“Entourage” confirms this view. Vince may not be a whiz at math, or even know how to drive or get messages off his phone — that’s what his entourage is for — but he is a genius of intuition. When he’s on his game, which is most of the time, he’s like a surfer for whom the world is a succession of perfect waves. He knows how to go with the flow because he intuits it where others don’t.

One of the most impressive things about “Entourage” has always been how its writers manage to compress so many interlocking story lines into an episode that typically runs 25 minutes. But the entourage — manager Eric; gofer and driver, “Turtle” (Jerry Ferrara); and Vince’s older halfbrother and cook, Johnny Drama (Kevin Dillon) — is beginning to fray at the edges, if not fall apart. The result is that the story lines are not quite so tightly and satisfyingly braided as before.

Johnny now has his own sitcom pilot, but his eternal role as Vince’s second fiddle continues with a run of comical bad luck. A giant billboard for the TV show appears on Sunset Strip, but the lights on it blow out so no one can see it after dark. Nor does anyone ever seem to recognize him, even when he’s standing in front of the billboard in broad daylight, which he does for several hours while making Turtle take photographs of him. He’s also the victim of a humiliating “Punk’d” style prank by Pauly Shore.

In the meantime, Vince’s increasingly cozy relationship with Amanda causes friction with Eric, since unlike with Ari, Vince wants to take all of Amanda’s calls, leaving Eric twiddling his thumbs. The boys try to rib Vince about his growing fondness for Amanda, but for once his perennially sunny temperament deserts him. Is he finally about to fall in love?

And then there’s Ari — how could there not be? He may no longer be Vince’s agent, but he’s forever in the wings, tossing temptations Vince’s way as he tries to lure his boy back. But the real surprise is the effect Vince’s desertion has on his former agent. Ari is in mourning. He can’t seem to get over the rejection. Worse, it’s affecting his performance at work. He’s lost his killer instinct. For example, he no longer enjoys firing people — imagine! In fact, at a certain point he is physically incapable of firing someone who absolutely must be fired. Yom Kippur is approaching, and Ari, prompted by his wife, is detecting signals from an inner planet he’s never heard from before, at least when it comes to business — namely, his conscience. Is he about to have a midlife crisis? Burst into tears? Surely, not. If Ari went soft on us, where would that leave the show?

bbernhard@nysun.com