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Basic Trope: A superpowered person has a child, and they develop powers as well.
Straight: The superheroine Hiroko (aka Fujita 1) marries Gadgeteer Genius and Muggle Gary Gear, their children develop wind based powers and a proclivity to engineering.
Exaggerated: Their daughter Cherry develops wind powers orders of magnitude stronger than his Fujita 1 and knows everything Gary does about engineering.
Downplayed: Cherry finds a mostly finished Transformation Trinket her father made, fixes it, and gains wind powers similar to her mom's.
Gary developed a gene sequencer he used on himself and Fujita 1 to isolate and distill their powers and knowledge, and ensure their Gattaca Babies have all their best traits and powers.
Gary and Hiroko got their powers from a genetic mutation.
Hiroko and Gary are Muggles, but when Cherry starts developing wind based powers and strong mechanical aptitude they both start developing these abilities in turn.
Superpowers work by draining the ability of those nearby to fuel their own, so having a superpowered person in your immediate family means you can't develop your own.
Subverted: Cherry has no powers and is frequently targeted for kidnapping because of this helplessness.
Until she spontaneously triggers them in a fit of emotion.
Or studies really hard and learns to build, repair and pilot one of her dad's suits of Powered Armor.
Parodied: Fujita 1 and Gary have over a dozen kids, each of which is progressively more Goo Goo Godlike, forcing them to abandon heroing in favor of corralling their unruly family.
Zig Zagged: Cherry has superpowers because of her parents, only it's all just a magical trinket she's been using, however the trinket was actually empowering her slow to mature powers, but these were really just effects of a Super Serum that's wearing off.
Enforced: All superpowers, no matter how they're gained, are absorbed into the parent's genome. Turns out humans have the natural superpowers of absorbing superpowers they are given.
Lampshaded: "Okay Hiroko, I've finished work on the crib. Are you sure it needs to be able to contain Fujita 5 scale hurricanes?" "Gary, my grandmother could make loose paper move, my mother could create stiff gusts of wind and I can tear the roof off a house. You see the progression, yes?" "Let me go get another counter-turbine."
Invoked: Hiroko and Gary want to make a Super Family Team, so they do all sorts of things to raise the odds Cherry is born with powers, like cosmic ray sunbaths and wearing lots of magical trinkets.
Exploited: Knowing Cherry would likely develop powers and be a target of kidnapping because of it, Gary develops a temporary power suppressor that lets Cherry have a normal childhood... all while they train her in combat and use VR to simulate how controlling her powers would be like. When she's inevitably kidnaped and goes 24 hours without the Power Nullifier treatment, she draws on this training to efficiently dispatch her captors.
Defied: Hiroko and Gary want to let Cherry choose whether or not to be a superhero, so they develop a machine that can De-power or Super Empower her once she's old enough to choose. They even make sure to let her experience heroic and muggle life to better decide.
Discussed: "Gary, if we have children they will likely inherit my wind based powers. Can we bring a child into the world knowing he or she will probably face the same challenges we will? Never even to know a life of normalcy." "We don't know that they'll develop your powers or gain my technical abilities, but regardless we can at least give them a loving family."
Implied:: Most superheroes have at least one other superpowered person in their family line, even if only distantly.
Deconstructed: Superheroines adamantly use birth control because the rigors of child rearing mean they essentially have to abandon their careers. Male superheroes with active sex lives are incredibly careful (or avoid it entirely) because it can lead to dozens of new emotionally unstable super kids down the line. A government agency is even tasked with tracking superhero hookups to track potential new supers born to them or muggles.
Reconstructed: Heroes and villains use this to create powerful Super Family Teams, evil governments create super "breeding camps" to fight rivals, and even good governments try to create stable marriages to help make a new generation of stable heroes.