Young adult fiction almost always features a protagonist who is a teenager or young adult for most of the story or series. This means that one of the largest problems YA authors face is the “Parent Problem,” that is, the problem of how to get their protagonists to have adventures without the adults of the community stepping in to protect them, the way actual responsible adults are supposed to.
Logically, there are really only four options: 1) The adults behave like responsible grown-ups who take on appropriate parts of the adventure and/or plot; 2) The adults behave like responsible adults, but the story problems revolve around things that most reasonable adults would expect a teenager to solve for themselves; 3) There are no adults around; or 4) The adults are irresponsible, incapable, incompetent, or outright evil.
Many story problems revolve around things that are too large for anyone, adult or not, to handle alone. There are plenty of books in which the dam breaks or a hurricane inundates the town; while the adults are busy coping with rebuilding, the teens and younger children cope in their own way with their parts of the problem. The problem is large enough that everybody has an appropriate piece to handle, so the young protagonist has plenty to do even though there are lots of adults around.
The second option is the method of choice for an enormous amount of present-day-setting YA. Adults cannot actually be on the high school basketball team; they can only coach. So if the story-problem is about winning the state basketball tournament, it’s fairly easy to keep the adults out of it (or make them part of the problem, see #4) Young adult and teen romances usually deal with high school dating problems; while an adult might reasonably give advice, one wouldn’t expect an authority figure to dictate who a teen could date or follow a pair of teens around to tell them when they should hold hands (and even if they did, there’d still be plenty of room for “but does he/she really like me?” angst). There’s a vast array of so-called “problem novels” that deal with teens coping with difficulties ranging from abuse to the death of a family member to their parents’ divorce. Sometimes, the protagonist gets adult help, sometimes not, but the thing all these stories have in common is that ultimately, the protagonist is the one who has to deal with the emotions involved, because nobody else can actually do it for them.
As for #3, there are two basic ways of having no adults around in a story: first, the young protagonist can be separated from the adults by accident or design (that is, he/she can be the lone survivor of a shipwreck or plane crash in the wilderness, or she/he can run away). In Hatchet by Gary Paulsen, the teen protagonist is the only survivor when a small plane crashes in the Canadian wilderness; Jean Craighead’s classic My Side of the Mountain is the story of a runaway trying to live in the woods on his own, and while adults occasionally pass through, the protagonist always has to consider whether they’re likely to drag him home before he decides to interact with them, and never lets them take over the responsibility that he has seized for himself.
The second way of having no adults around is, of course, to kill them off or have them mysteriously disappear. Killing off the parents early on is a time-honored way of forcing a young protagonist to be responsible for him/herself; just look at all the fairy tales that start with the main character being orphaned. Mysterious disappearance is another good way of getting rid of the adults who’re supposed to be looking after things (and can do double-duty by giving the protagonist someone to go out looking for). The two are often combined, as when one parent goes off somewhere and vanishes, and then the remaining parent dies or is incapacitated. In modern stories, divorce is sometimes used as a less extreme way of disposing of at least one parent; like mysterious disappearance, it gets one adult out of the way while leaving open the possibility that the missing parent will return.
The trouble with killing off the parents, especially in a modern-day story, is that it doesn’t get rid of all the other adults who could or should take responsibility for a child or teenager. Families seldom exist in isolation, and most communities expect some adult to step in and take care of an orphaned child. This is particularly true if the parents are killed off when the protagonist is very young; somebody has to take care of a two-year-old, or the toddler won’t survive. Once the protagonist is old enough to get by on his/her own, the author can sometimes arrange to have the main character’s entire village wiped out by bandits, an invading army, plague, or a dragon, leaving the teenaged hero or heroine with no one to depend on but themselves, but this kind of wholesale slaughter doesn’t always fit the story the author wants to tell.
This brings us to option #4, the adults being irresponsible, incapable, incompetent, or outright evil.
This one can be used alone – in comedies, in particular, the bumbling, incompetent adults who have to be rescued by the kids are a perennial favorite – or in combination with killing off the parents, as with all those other fairy tales full of evil stepmothers and wicked uncles who’re after their ward’s fortune or title. Often, the supposedly responsible adults who take the orphan in turn out to be resentful, neglectful, or incompetent (or all three at once), like Harry Potter’s aunt and uncle, or Jane Eyre’s aunt and most of the adults in the boarding school she attends. Corrupt, venal, or abusive masters are a staple of fiction in which the protagonist is working as an apprentice, rather than living with family. There are also stories in which the “somebody” who takes responsibility for the orphaned child is unexpected or unconventional, and that’s the source of the story, as when Mowgli is adopted by wolves and raised by the animals in the jungle.
And then there are the stories where only the protagonist is capable of achieving the story-solution, because he or she has some power or ability that the adults lack. In a realistic modern-day story, this might be a talent for something like chess or music; in fantasy, the protagonist may be the subject of a prophecy or have some rare magic power; occasionally, one finds a story in which children have a power or ability that is lost at puberty or when they become adult or reach some other major life-milestone. The adults can be as competent and responsible as they like, but only the protagonist can win the game/pull the sword from the stone/kill the evil wizard/etc.
Historical fiction, science fiction, and fantasy allow for a final option: finding or inventing a culture in which teenagers are allowed and expected to do things that modern society reserves for adults. This can solve most of the Parent Problem quite handily; if a society considers people more or less adult at sixteen, then the sixteen-year-old hero can go off and have adventures like every other adult. Lots of fantasy takes this way out, either by basing the story on a real-life time and place where adulthood arrived much sooner than it does in the modern world, or by inventing an entirely new society that works the way the author needs it to. The Hunger Games postulates a future dystopia in which teens are deliberately put at risk as a way of enforcing the government’s control. And SF/F allows for all sorts of new ways to implement the four basic solutions, from spaceship crashes to teleportation accidents.
I have to finish by pointing out that the Harry Potter books makes use of nearly all of these methods at once: the hero is an orphan, the subject of a prophecy; the aunt and uncle who take him in are neglectful/incompetent; the other adults in his life cover the range from obviously incompetent (Minister Fudge) to supposedly-responsible but busy dealing with the Big Picture (Dumbledore) and thus leaving the kids largely to their own devices; he and his friends spend much of the final book as, essentially, runaways; etc.