When Grey's Anatomy actor-director Debbie Allen recently attended the bat mitzvah of a neighbour's daughter, she didn't recite any Torah passages but still wound up the centre of attention.

"I've had people ask for my autograph, but this was a whole different level," she recalled with a laugh. "People were taking pictures of me – they wanted selfies. They all had so many questions about storylines and what was going to happen next. Child, I was the star of the show!"

Grey's, which Allen now also runs as executive producer in addition to playing Dr. Catherine Avery, has managed to hook younger viewers, returning the show to the cultural conversation more than a decade after Meredith Grey and Dr. McDreamy donned their first set of scrubs. Thanks to Netflix, Grey'creator Shonda Rhimes's expanding influence and the surprisingly retro tastes of teens, the show has become the rarest of entertainment unicorns: a broadcast show ending its 13th season with both ratings and relevance on the rise. It has been renewed through Season 14, and ABC executives have said that as long as the creative team is committed, they'd love to see it surpass ER's 15 seasons on the air.

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Andy Kubitz, ABC's executive vice-president of program planning and scheduling, said the show has ranked in the top 10 among viewers 18 to 34 for the past six years, jockeying with the likes of This Is Us, The Big Bang Theory and Modern Family. Among teens (in TV terms, viewers 12 to 17), it is No.11, but has held that audience far longer than shows such as Empire or Glee. In fact, its teen ratings have increased 12 per cent over last year.

Allen said the show's young viewers, many of whom were infants when it debuted in ABC's mid-2000s lineup alongside Lost and Desperate Housewives, have arrived through serendipity, not deliberate effort.

Grey’s Anatomy actor-director Debbie Allen says the love stories running through the show help attract teen viewers. Richard Cartwright/ABC

"I think they are connecting with the reality of the situation. Grey's is rooted in reality," Allen said. While not as frothy as more recent Rhimes shows such as Scandal and How to Get Away With Murder, she added: "There certainly is a lot of love story going on. As a young teenager, you are at an age when you are starting to notice that this guy or that guy likes you. And it's a very dynamic turning of stories. So they really respond to that."

The show's fountain-of-youth ratings are especially striking when one considers how dramatically TV viewing has changed since the show premiered. Overall broadcast prime-time ratings have plunged more than 30 per cent over the past decade as one distraction after another – video games, mobile devices, streaming services – has atomized the live TV audience.

Kevin Goetz, founder and CEO of Hollywood research firm Screen Engine/ASI, considers the teen audience "the most difficult segment to reach and predict in the entire entertainment business." Entire networks have made it their mission to cater to teens and twentysomethings, as youth-obsessed advertisers chase consumer loyalty from the time viewers take in their first frame of Dora the Explorer. ABC's cable-network sibling, previously called ABC Family, went so far as to change its name to Freeform and started releasing some shows in binge-quantity batches in order to seem au courant. The youth-focused CW Television Network, home of Jane the Virgin and The Flash, has rebooted Archie Comics characters in the new series Riverdale. Even Netflix has made this group a cornerstone of its shock-and-awe original programming strategy, drawing a huge teen crowd with shows such as 13 Reasons Why and Stranger Things.

Even more noteworthy are shows Netflix has acquired from networks. Full House, a hit for Nickelodeon in linear reruns, joined the Netflix lineup and did well enough to get a full-on series reboot, following the path of Arrested Development and Gilmore Girls. The streaming service has also been a conduit for network classics such as The Office and Friends, served up one episode after another via the Netflix auto-play feature, screen media's answer to the Pez dispenser.

Kubitz pointed out that the 2009 Netflix deal for Grey's was one of the first ABC made with a streaming service other than Hulu (which is partly owned by ABC's parent company, Disney). Being so early in the streaming revolution meant fewer limits, so the show has streamed for eight years, whereas newer titles often cycle on and off. Digital exposure has also overlapped with linear syndication on networks such as Lifetime. While data are notoriously scarce on Netflix shows, a person who has seen the numbers said the pilot episode of Grey's Anatomy is viewed hundreds of thousands of times a month. "It's incredibly bingeable," Kubitz said. "People just want to curl up with a blanket and a bowl of popcorn and watch Grey's."

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One such curler-upper is my daughter, Margot, who could easily have been one of the eager fans stalking Allen at that bat mitzvah. So I decided to do as Hollywood marketers do and convene my own focus group.

Grey’s cast and crew live tweet the show every week, stoking interest by interacting with fans. Richard Cartwright/ABC

When I asked them why they tuned in, Margot and her friends used words such as "timeless" and "modern" to describe the show. "The show is so real," Dana Cohen, 13, said. "Bad things happen to the characters on the show, just like they happen in real life. Also, it has the perfect balance of the drama between the characters and the medicine."

There is indeed plenty of hospital action, though less than in most episodes of ER or more recent adult-skewing medical dramas such as Code Black or The Knick. Abscesses develop. Surgeries are performed. Characters talk the talk. But they also hook up and cheat on each other and have thorny workplace dilemmas, often to a shimmering, Starbucks-ready pop soundtrack. They form alliances, get promoted or passed over.

And, of course, they occasionally die: In a still-controversial plot twist in 2015, Patrick Dempsey's character, Dr. Derek (McDreamy) Shepherd, died from injuries suffered in a car accident.

Allen said the creative team has never wanted to construct storylines with binge-watching in mind, even though they appreciate that many young fans catch up in bulk on the first 12 seasons of the run. "We stay in the moment," she said. "That's what makes us sharp. We take the same approach as actors: If you got applause yesterday, you have to forget about it and play it today, and tomorrow hasn't happened yet."

The other reality for Grey's, ABC and TV networks in general is that they still make billions of dollars from advertising as sponsors stick with the traditional model. That tends to favour serialization, the opposite of how Netflix, a subscription service, releases full seasons at a time. With that week-by-week approach, Rhimes & Co. have perfected a means of stoking interest: live tweeting. Cast and crew – often including Rhimes, who has 1.47 million Twitter followers – watch Grey's live, all while interacting with fans and learning from viewer reactions they hadn't anticipated.

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Twitter's launch in 2006 (after Season 1 of Grey's Anatomy aired) helps explain how a show built on the same model as I Love Lucy has become a magnet for middle-schoolers who have never bothered to find MTV on their cable dial. Allen remembered several instances in which the social network altered the show's course. For example, it helped determine a key bit of timing involving Callie Torres and Arizona Robbins, married doctors played by Sara Ramirez and Jessica Capshaw.

"The love affair between them was the most popular gay relationship ever televised," Allen said. "It took a really long time for Shonda to break them up. Millions of people didn't want anything to come between them."

Allen, who became known for acting in 1980s hits Fame and A Different World before expanding into directing and producing, sees some risk in turning what used to be a one-way medium into a dialogue.

"The danger for actors is that they can forget that they're playing characters," she said. "People will react to this storyline or that storyline, and an actor can feel personally involved. They need to remember: If your character does something people hate, it's not about you! But that's just how our audience connects with the characters on Grey's. They're like family."