It has been almost a month since the very famous, presumably rich and remarkably still anonymous British street artist and trickster Banksy began making good on his word to spend October festooning the streets of New York with his art. 

Nearly every day, as part of what he called his New York “residency,” Banksy has posted to his website and Instagram a photo of a new piece — a wry scrawl, a cheeky silhouette, a cartoony sculpture, an installation — and identified its location by neighborhood. He has wended through all five boroughs with the project, titled “Better Out Than In” — although Staten Island got only one Banksy, and it was a video. As soon as a post goes up, little armies of people set out to find it — Banksy’s work sells for hundreds of thousands of dollars, and here it was hanging free — twittering in triumph when they do.

Borough by borough, and sometimes neighborhood by neighborhood, reactions differed every time a Banksy popped up. In a way, it took this Englishman to remind New Yorkers that parts of our city remain distinct as foreign lands.

In East New York, local residents charged viewers $20 for a peek of a stenciled beaver. In TriBeCa, at a stencil of the World Trade Center towers, people laid flowers. In Hell’s Kitchen, exotic dancers preened before the image of a lovelorn swain at Larry Flynt’s Hustler Club. A piece on the preservationist-friendly Upper West Side was quickly sealed behind plexiglass. On the Lower East Side, people ripped off the doors of a painted car. In Queens, and in Red Hook and Williamsburg in Brooklyn, images were swiftly bombed by taggers: local street artists incensed that an Englishman had trod on their turf.

Mike Ellyson, 33, an artist who lives in East Williamsburg, said he watched in awe a few days ago as a worker began scrubbing a Banksy tag off a laundromat wall, causing onlookers to yell, imploring him to stop.

“I think it’s amazing — people fighting over a laundromat, Mr. Ellyson said.

Though Banksy works have shown up on private buildings, the Police Department has gotten no official complaints, a spokesman said, adding that apprehension was difficult because “we don’t know who Banksy is, if he exists at all.” Mayor Michael R. Bloomberg’s tut-tut response that graffiti was “a sign of decay and loss of control” only gave the project more of a boost. 

The project has also stirred up animosity. This city has bred some serious street artists, after all, few of whom have garnered the fame enjoyed by Banksy.

“I think he’s a fraud,” said Tiffton Meares, 31, a chef from Williamsburg, as he wandered past the Banksy stencil of the twin towers in a TriBeCa alleyway this past weekend. “My friends believe it is a ploy to get New York cool again.”

Mr. Meares conceded that some of Banksy’s pieces were “poignant,” but expressed disdain for Banksy’s followers, some of whom he said sat in pigeon droppings to pose for photos alongside the TriBeCa piece, even after a pug had relieved itself on the wall.

Banksy fans lured to hard-bitten East New York, Brooklyn, where many live below the poverty line, were taken aback when they encountered a group of tetchy residents, who had shielded the little graffiti beaver with cardboard and were demanding pay per view.

“We’re trying to get some bread — this is my hood,” said one man agitatedly, his response caught on video, before adding, no doubt accurately, “Y’all wouldn’t come here if this wasn’t here.”

After the crowds drifted away, the beaver’s face was scoured off and the piece was all but forgotten.

Not so for East Williamsburg, where a tagger was tackled to the ground by a building manager after he scrawled over Banksy’s image of geishas on a bridge. The building’s owners, one of whom wrote about the adventure, hired security guards and later installed plexiglass and a roll-down gate, which is now open daily on a viewing schedule for the dozens of people stopping by.

“A lot of people come to the neighborhood,” said the manager, Jose Goya, 33. “Now we have something to show them. Something nice.”

Ruben Diaz Jr., the Bronx borough president, was also thrilled by the Banksy-generated attention — at least at first. In mid-October, Banksy graced the South Bronx with a fiberglass replica of an ill-tempered Ronald McDonald watching as a dirty ragamuffin, played by an actual human, shined his outsize shoes. Delighted, Mr. Diaz likened Banksy to a “contemporary day Picasso.”

Then Banksy unveiled his second Bronx offering: a stencil of a schoolboy spray-painting the words “Ghetto 4 Life” as a butler proffered a tray of paint cans. Furious, Mr. Diaz fired off a statement saying the word “ghetto” was a slur, and wagging a finger at Banksy for perpetuating “outdated negative stereotypes.”

Yet the building’s owners cooed about the work and, determined to protect it, first hired security guards to watch over it and then set a thick sheet of glass over it, and a roll-down gate.

All of which struck several residents of the Bronx, birthplace and home to famously dazzling street art, as downright absurd.  

“You go around the Bronx and there are pieces grander than that, and no one goes over them because they got respect,” said Miguel Delgado, 30, a chef who lives in the neighborhood. “They don’t respect him because he’s not from here.”

Not every borough got equal attention. Queens has received two pieces so far, one of which, a sculpture of a Sphinx, was quickly sold off to a gallery. The Staten Island-inspired video, location as yet to be determined, starts as a close-up of an anthill and pans out to reveal a woman’s vulva.

Pieces were largely concentrated in Lower Manhattan, which was also treated to, among other Banksy sights, “Sirens of the Lambs,” a truckload of stuffed animals, slaughterhouse-bound and mewling, and, this past weekend, an installation involving the Grim Reaper.

“It’s genius in the sense he has people gathered staring at a bumper car,” said Tom Griffin, 34, an artist, as he joined a crowd of hundreds in NoHo on Sunday night to gaze as the Grim Reaper motored about an empty lot in, yes, a bumper car.  

Sunday’s installment, on a wall in Greenpoint, Brooklyn, simply read “this site contains blocked messages,” an apparent reference to an op-ed written by Banksy denouncing 1 World Trade Center. Banksy sent the article to The New York Times, a spokeswoman said, adding that editors asked him if he would create art of what kind of tower New York should get instead. What he ended up submitting, she said, “wasn’t at all what we were expecting, so it was rejected.”

With Banksy’s “residency” coming to a close — Halloween is to be the last day — tourists and local residents alike are still racing about town trying to catch sight of what is left of it.

On the Upper West Side, the stencil of a child striking a standpipe with a hammer, now protected by plexiglass, drew fans all weekend.

On Sunday, the crowd caused a man, who had an infant strapped to his chest and was pushing a toddler in a stroller, to stop short.

“Is that supposed to be the Banksy thing?” he asked. “Man, that’s horrible. God, the hype.”

He refused to give his name, and would reveal only that he spent his childhood downtown.

“I grew up with real graffiti artists,” he huffed as he strode away, stroller in front of him, his baby’s legs bobbing.