CHICAGO — It is Saturday morning, and 10-year-old Henry Hailey is up at the crack of dawn. Still in PJs, his microphone-equipped headphones glowing blue in the dim basement, he fixates on the popular online game “Fortnite” on a large screen.

“What?! Right as I was about to finish it, I died,” he calls out disappointedly to his friend Gus, a fellow fifth-grader playing the game from his home just a few blocks away. “Dude, I should NOT have died.”

The digital battles resume, and Henry’s enthusiasm never wanes. Would he play all day if his parents let him? “Probably,” he concedes with a slight grin.

But they do not. Like many other parents, the Haileys are on a reinvigorated mission to limit screen time for Henry and his 15-year-old brother, Everett. For some parents, it feels like an exercise in futility. They are busy, overwhelmed and tired of the fight against increasingly omnipresent screens.

Getting Henry off screens has been a constant battle, his parents say. “Then once he’s off, there’s a lot of complaining and grumpiness for a while as we try to coax him to do something else,” says his mom, Barb Hailey. “He’s upset. Mom is a crank. What is it all for?”

The goal, experts say, should be to help kids learn to manage their own time as they get older and to stay physically active and socially connected as much offline as on. But parents in many American households are finding the power struggles — tantrums, withdrawal and, in some cases, even school and discipline problems — difficult, especially as more kids get access to screens at younger and younger ages.

A survey of 13- to 17-year-olds released this fall by the nonprofit Common Sense Media found that 95 percent of U.S. teens have their own mobile device. Seventy percent of them check social media several times a day, up from 34 percent in 2012. More than half say that their devices distract them from homework or the people they’re with.

Some tech companies now at least acknowledge concerns about over-use and outright abuse of digital media. Apple instituted a “Screen Time” function in its latest iPhone software. It monitors app use and allows users — or their parents — to establish limits. Google For Families and Google Play, found on Android phones, and various independent apps also allow parents to monitor and set some restrictions.

But those features aren’t enabled by default, so new limits can come as a shock to those on the receiving end.

That happened late this summer in the Hailey household on Chicago’s North Side after dad, Allen Hailey, began watching the amount of time elder son Everett was spending on Wi-Fi. The teen was clocking more than four hours a day on sports videos, games and chats with friends on social media.

“I don’t think he had any idea how much time he was spending online,” says the father, who decided to block both boys from Wi-Fi during certain hours. He tested it out one night without warning.

One minute, Everett was talking to a friend on social media. “Then it went out,” says the teen, who immediately complained aloud about the injustice of it all. Dad held firm and told him he needed to read a book or go outside to shoot hoops.

“I didn’t do anything wrong to deserve that,” Everett still insists. “If I get my work done, I think I should have my own time.”

Researchers who study these trends generally refrain from using the word “addiction” when it comes to screens, as it’s not an official diagnosis in the mental health world. But this summer, the World Health Organization added “gaming disorder” to its list of afflictions. That is gaming that severely interferes with relationships, school and work. The diagnosis is still under review by U.S. health authorities.

Sometimes, experts say, digital immersion exacerbates an existing condition, such as depression, anxiety or issues with body image. That’s why teens who attend treatment at Newport Academy, a residential rehab and mental health program with sites across the country, must check their digital devices at the door when they arrive.

“Almost always, one of the symptoms is an excessive amount of time on smartphones,” says Heather Senior Monroe, a Newport Academy administrator and licensed clinical social worker. “And it’s usually a large symptom.”

A small number of facilities have sprung up or added programs to specifically address the abuse of digital media. And in Washington state, a hub of high tech, there’s a 12-step group called Internet & Tech Addiction Anonymous .

From Henry and Everett’s perspective, the real problem is that their parents seem stricter than most.

Like a lot of teens, Everett often uses multiple screens in the evening. He saved his own money to buy himself an older-model iPhone — “to fit in,” he says — and also uses a Chromebook laptop for homework. At his age, his mom says, his screen habits may be “a lost cause.”

But she keeps working on limits for Henry. Games are not allowed on weekdays. And he gets screen time only if all his homework is done.

Experts say time limits can help but are sometimes a moot point given how deeply technology is “embedded in our daily life,” says Sarah Domoff, a psychologist at Central Michigan University.

Instead she asks parents: How are your children doing in school? Are they active and physically healthy? Are they connecting with others in positive ways?

She does have a few basic rules, including limiting screen time for younger kids to the educational stuff. She also suggests making bedrooms “screen-free zones,” even for teens. (Other experts, at the very least, advise keeping devices out of rooms overnight to avoid late-night shenanigans or other sleep interruptions.)

The Haileys sheepishly note that Everett routinely multitasks in his room with one eye on the Chromebook and often the other on his phone. “I think we’re kind of wimps,” Barb Hailey says. Henry doesn’t have a phone — yet.

But phones and other screens are not allowed during meals — a limit both boys seem to appreciate. Everett says when they go out to eat, he happily leaves his phone in the car and marvels at the number of other families who are at the table with screens. “That just looks bad,” he says.

Managing all this is no easy task, even for experts such as Sierra Filucci, executive editor of parenting content at Common Sense Media, an organization that helps families navigate the digital world.

Her own 12-year-old son, like Henry, is a fan of “Fortnite.” She’s witnessed the “bad attitude” when he’s asked to get off the game and take out the garbage or find something to do that doesn’t involve a screen. But she also sees the positives — connections he’s made with new friends at school, for instance. For her, the question is: “How do we help him self-regulate?”

Some parents simply put off getting their kid a phone. Jacqui Koch, a college professor and mother in Wilmette, Illinois, had her sixth-grade daughter sign a pledge to wait until eighth grade for a smartphone — part of the national “Wait Until 8th ” movement. Her daughter didn’t put up much fuss, in part because mom has limited tech use for years.

“We are definitely not the norm of what we’re surrounded by,” Koch says, noting that she saw a “huge uptick” of kids with phones in fifth grade. Now some parents she knows are trying to backpedal, “and that’s hard,” she says.

The idea is that Wait Until 8th and events such as the National Day of Unplugging , an annual event in March, will make screen limits more socially acceptable and less like an adult-world imposition on kids.

Another key: Parents setting limits with their own devices.

When Allen Hailey is on his phone while watching a football game, Everett is quick to tell him that he’s on his phone too much. “He gets really mad,” Everett says.

When mom comes home, she says she tries to put down her phone, though it’s hard not to check emails for work. “Let me just check in,” she’ll say — and before long finds herself on Instagram and Facebook.

“You can go down the rabbit hole so easily,” Barb Hailey says. “Then you get it thrown back in your face.”

It’s not an easy balance to strike, but all the Haileys are trying. “We may not like it,” Everett says, as his little brother nods. “But we know it’s for the best.”

Their dad still wants his boys to read 30 minutes a day. After he put the limits on the Wi-Fi, Everett went out and bought two books, then texted Dad photos of them to prove he’d done it.

The boys do regularly hang out with friends in person, and both play soccer. Everett plays the saxophone. Henry plays trumpet and recently took up the drums.

Mom laughs: “So when we say, ‘Get off the screen’ and he goes and plays the snare drum, we have to live with that decision.”