Third Line, Some Waiting

"Meanwhile, on Cylon Occupied Caprica"

Somewhat of a variant on Two Lines, No Waiting, this is a minor C Plot on a show that is somewhat removed from the main plots, often geographically (but sometimes temporally), that recurs every episode but is only featured very briefly in each episode. It may eventually link up with the main plot, or it may not. What differentiates this from a standard B Plot is that if you skipped those five minutes every episode, you would not miss a thing until possibly much later in the show.

If the show is composed entirely of C Plots being alternated this way, then it's Four Lines, All Waiting.

Examples of Third Line, Some Waiting include:

Anime and Manga

The plot involving Nabeshin and Pedro and Pedro's effort to reunite with his sexy wife in Excel Saga.
Ghost in the Shell: Stand Alone Complex 2nd GiG had two major plot lines as well as episodes devoted to individual missions. In the end, they all tied into each other. The film that followed which was very obviously planned as a third season tried to up the ante.
Once an episode, Samurai 7 has a "Meanwhile, at the Mobile Oppression Fortress" scene that focuses on Ukyo, son (actually clone) of the Evil Overlord. His plotline eventually links up with the main one around episode 18, at which point the show takes a sharp upwards turn in quality.
Baccano!! covers three plots taking place a few years apart, with the 1931 Flying Pussyfoot plot being the centerpiece. It's only around half way we find out the truth about the mysterious Rail Tracer, and one character introduced in the very beginning only becomes an active player in the Gambit Pileup near the end.
Mahou Sensei Negima for the Magic World arc has the main line following Negi, a second line for Yue and on rare occasions a glimpse back to Mahora to see how things are developing there. As of now (Chapter 287) there's about two lines with Yue having met back up with Negi finally, while Mahora is gearing up to deal with whatever Fate is going to do upon reentering the real world. Then there's a third line following Anya and Asuna while they're held captive by the Big Bad.
In One Piece, the plotline about Ace's search for Blackbeard and Shanks meeting Whitebeard is slowly advanced between the arcs about Luffy's adventures, which finally gains significance in the main storyline when Ace catches up to Blackbeard but Blackbeard captures Ace and sells him out to the Marines, prompting Luffy and Whitebeard to attempt a rescue.

Literature

A Song of Ice and Fire has chapters that focus on a character currently on a different continent than everybody else. It's clear that it'll be important eventually, but as of four books, she has had no interaction whatsoever with any other major character and only recently has she even really been mentioned by POV characters bar a few fleeting references in the first book.
- According to The Other Wiki, the HBO adaptation is already setting up Daenerys's storyline like this.
- Dany is an odd example; decisions made in the main plot actually do quite clearly affect her. The first major example that springs to mind, if we don't include Ser Jorah's real purpose for being there, is when Robert Baratheon learns of her new husband and his 50,000 warriors and immediately raises the bounty on her head. This news takes a few months to cross the ocean, so it's some time before the attempt is made on Dany—less attentive readers might not have made the connection at all. It's also the reason that The Reveal of Barristan Selmy's defection is so shocking—it's literally the first time someone from one of the other two plotlines has had direct contact with her.
- By A Dance With Dragons more characters from Westeros are beginning to have influence on the geographical area that Dany is in, leading to more continuity between plots.
A Deepness in the Sky by Vernor Vinge has this, with the Qeng Ho/Emergents and the Spiders as the A and B stories, and Pham Nuwen's biography in slot C.
The Prophecy of the Stones does this between the three main protagonists and the Supporting Leader on their separate quests, and a seemingly unrelated Parisian girl from the present. But the twist is that the Parisian girl is dreaming of the future .
The Belisarius Series has a humorous C plot in The Dance of Time where a luckless Malwa assassination squad attempt to assassinate the main characters. They travel some three thousand miles from India to Greece, to Egypt, to Persia and back to India in a long series of missed opportunities.

Live-Action TV

On the first season of the new Battlestar Galactica, each episode had about five minutes of the Mauve Shirt Helo's adventures stranded on Cylon-occupied Caprica; everyone else assumed he was dead.
- Season 3 featured Baltar on the basestar and season 4 had Starbuck's trip to find Earth.
Most episodes of Malcolm in the Middle would have a unrelated subplot featuring Francis first at a military academy, then in Alaska, then on a German-run dude ranch. Very rarely would these at all connect to the main plot.
Heroes has a lot of very unconnected B Plots, but two stand out: Hiro stranded in Shogunate Japan and the Central American Wonder Twins.
- Not to mention Peter being stranded in Oireland.
- One of the problems with Season two was that all of the above mentioned storylines happened at the same time, resulting in Four Lines, All Waiting.
The whole "a traitor is contacting Seska" thing from Star Trek: Voyager Season Two.
CSI often has a background C Plots about the character's personal lives.
A lot of That '70s Show episodes have three storylines per episode: the A and the B story about the teenagers, and the C plot about the adults, mostly the Formans.
Season two of Lost has the Tailie plot for the first seven episodes. You could skip these segments until they meet the main survivors and not really miss anything.
- The flash-sideways. You have to wait until the season's eleventh episode for them to have any impact on the main plot, and the central revelation of the episode (that they're remembering love) has little to do with the earlier flash-sideways. You could skip them all until "Happily Ever After" and miss nothing.
  - ...until the Series Finale reveals the true, massively important nature of the flashsideways: it's the afterlife.
In Chuck, Ellie and Awesome's trip to Africa in "Chuck versus the Role Models" is completely removed from the A and B plots and only serves to set up next episode in the last minute.

Web Comics

Schlock Mercenary: Meanwhile, at the Galactic Core...
During the first few acts of Homestuck, the subplot involving the Wayward Vagabond and his fellow refugees from Prospit and Derse fills this role. It's set in the future upon a post-apocalyptic earth, but the characters are able to interact with the protagonists via technology. However, as more and more characters are introduced in later acts, the plot moves in the direction of Four Lines, All Waiting.

Western Animation

Beast Wars had some of these in the form of long-simmering, foreshadowed schemes: Tarantalus building up a lair and an escape ship, Dinobot wrestling with the implications of the original Golden Disk (not the alien one), Blackarachnia gathering components for Transmetal-2 transformation...
The X-Men cartoon had several of these, most notably Magneto and Professor X in the Savage Land throughout season two.
The Ice Age films have Scrat, which is a separate plot (if a bunch of gags involving an unlucky squirrel qualifies as plot...) from the other main characters. Yet is the most beloved part of the franchise.
Occasionally, along with a project Phineas and Ferb do and Doof's regular plan, Candice may have her own subplot. In "The Great Indoors", Doofenshmirtz makes it rain so a Mexican soap opera he's been watching ("It has three simultaneous story lines that interconnect. Genius!") won't be preempted by a soccer game, so Phineas and Ferb build a biosphere to help the Fireside Girls earn their Desert Exploration merit badges. Candace puts off her efforts to bust her brothers when Jeremy thinks the biosphere would be a great place to have a picnic, as she wants to find out why he likes her.