Question: Powered by the Apocalypse (PbtA) is a role-playing game system used for what fantasy tabletop roleplaying game?

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Starshield: Starshield was a proposed trilogy of galactic fantasy novels written by Tracy Hickman and Margaret Weis, and was envisioned to spin off a tabletop roleplaying game and an online strategy game.  Only two of the three novels have so far been released.

Dungeon World: Dungeon World is a fantasy tabletop roleplaying game.  Created by Sage LaTorra and Adam Koebel, the game uses the Powered by the Apocalypse engine originally designed for "Apocalypse World" and used in "Monsterhearts" and other games.  The game is advertised as having old school style with modern rules.  The text of the game was released under the Creative Commons Attribution 3.0 Unported License.

One-Roll Engine: The One-Roll Engine (or O.R.E.) is a generic role-playing game system developed by Greg Stolze for the alternate history superhero roleplaying game "Godlike."  The system was expanded upon in the modern-day sequel, "Wild Talents," as well as the heroic fantasy game "Reign" and the free horror game "Nemesis."  A simpler version was used for "Monsters and Other Childish Things".  The One-Roll Engine is notable for its unique dice rolling system in which matched values on ten-sided dice (d10s) determine all variables of a check in a single roll.  This eliminates, for example, the separate initiative, hit location and damage rolls common during combat in other systems.

Starfinder Roleplaying Game: The Starfinder Roleplaying Game is a science-fiction/science fantasy role-playing game published by Paizo Publishing.  It is built on Paizo's previous game, the "Pathfinder Roleplaying Game", both in its game mechanics and universe, but adapted to a more futuristic style than its fantasy predecessor; game content is intended to be easily convertible between the two systems.  Like its predecessor, the "Starfinder RPG" supports adventure paths and other material written by Paizo and third party publishers.

Simple System Table-Top RPG: The Simple System is a card based Tabletop role-playing game system that was funded using Kickstarter in May 2014.  The Simple System uses reusable double-sided Character Cards for each player (up to 5 players), Skill Cards and Item Cards with complete rule text to represent commonly used skills, weapons and other items.  In addition Life and Dying Cards shows the Health Status of each player.  The dice used in other Tabletop roleplaying games are swapped for a intriguing Resolution Deck that not only indicates success and failure of any attempted action, but also indicates directions, damage and turn order when needed.  The Simple System includes cards (Hero, Story, and Complication Cards) for the Game Master to reward and punish players for interesting choices and unlucky resolutions.

Stormbringer (role-playing game): The Stormbringer fantasy role-playing game published by Chaosium puts the players in the world of the Young Kingdoms, based on the Elric of Melniboné books by Michael Moorcock.  The game takes its name from Elric's sword, Stormbringer (though one edition was published as "Elric!")  and uses the Basic Role-Playing game system, a percentile-dice-based system used in many role-playing games designed by Chaosium.

Mouse Guard Roleplaying Game: The Mouse Guard Roleplaying Game is a tabletop role-playing game created by Luke Crane based on the Mouse Guard comics and his own Burning Wheel system.  It won the 2008 Origins Award for best roleplaying game and numerous Indie RPG awards, as well as being silver winner for three ENnies and shortlisted for the 2009 Diana Jones Award.  Boom!  Studios has announced its imprint Archaia Entertainment will release the second edition of the game in 2015.

Dungeons &amp; Dragons: Dungeons & Dragons (abbreviated as D&D or DnD) is a fantasy tabletop role-playing game (RPG) originally designed by Gary Gygax and Dave Arneson, and first published in 1974 by Tactical Studies Rules, Inc. (TSR).  The game has been published by Wizards of the Coast (now a subsidiary of Hasbro) since 1997.  It was derived from miniature wargames with a variation of the "Chainmail" game serving as the initial rule system.  "D&D"'s publication is commonly recognized as the beginning of modern role-playing games and the role-playing game industry.

Star Wars: The Roleplaying Game: Star Wars: The Roleplaying Game is a role-playing game set in the "Star Wars" universe, written and published by West End Games (WEG) between 1987 and 1999.  The game system was slightly modified and rereleased in 2004 as "D6 Space", which used a generic space opera setting.  An unrelated "Star Wars" RPG was published by Wizards of the Coast from 2000 to 2010.  Since 2012 the official "Star Wars" role-playing game is another unrelated game, published by Fantasy Flight Games.

Powered by the Apocalypse: Powered by the Apocalypse (PbtA) is a role-playing game system developed for the 2010 game "Apocalypse World" and also used for "Dungeon World", "Monsterhearts" and numerous other RPGs.  "Apocalypse World" won the 2010 Indie RPG Awards for "Most Innovative Game" and Dungeon World won the 2013 ENnie award for "Best Rules".

Supporting paragraphs: Powered by the Apocalypse Dungeon World
Answer: Dungeon World