"Branded" (烙らく印いん Rakuin) is an archetype introduced in Lightning Overdrive.
Similar to "World Legacy" throughout Series 10, the "Branded" cards serve as a connecting narrative thread between many of the themes introduced throughout Series 11, ("Dogmatika", "Despia" etc.), and detail major plot developments in the Abyss storyline through their artworks.
Despia" (デスピア Desupia) is an archetype of DARK Fairy and LIGHT Fiend monsters introduced in Dawn of Majesty.
"Despia"/"Despian" is a combination of the words "despair", "death", and "thespian". The names of "Despia" cards stems from theatrical elements and drama. The theatrical theme of the "Despia" archetype is fitting, as these monsters kept up the facade of a holy Church for a long time, as if they were playing a theatrical fiction, before revealing their true colors.
Most of the "Despia" cards consist of corrupted versions of the "Dogmatika" monsters. This may have been started with the events depicted in the artwork of "Dogmatikalamity", where "Dogmatika Maximus" opens a portal to the Hole.
Playing style
The "Branded" archetype is an archetype of Spell and Trap Cards that support the Fusion-based playstyles of "Fallen of Albaz" (and its related cards) and the "Despia" archetype. The three series of cards forms an overarching playstyle typically called "Branded Despia"; within Branded Despia, "Branded" cards serve as the Deck's main playmakers, and accessing "Branded" cards via "Despia" monsters and "Albaz" Fusion Monsters composes the Deck's primary resource loop.
The "Despia" archetype is a Fusion-focused archetype, and is a part of an overarching playstyle, typically called "Branded Despia", that encompasses "Despia", the "Branded" archetype of Spell & Trap cards, and the "Fallen of Albaz" Dragon form Fusion Monsters (and their dedicated support cards). Within Branded Despia, "Despia" provides the Deck's Main Deck starters and Fusion Material fodder.
Generally speaking, "Despia" cards and their specific "Branded" support cards generically support Level 8 or higher Fusion Monsters, while specific "Despia" cards provide support to "Branded" or "Albaz"-related cards, connecting it to the other two card series in Branded Despia.
The primary starter of "Despia", and therefore of Branded Despia as a whole, is "Aluber the Jester of Despia", who searches a "Branded" Spell/Trap when Summoned. The main search target for "Aluber" is the Fusion Spell "Branded Fusion", who can Fusion Summon "Albion the Branded Dragon" or "Lubellion the Searing Dragon" using materials from the Deck. From there, "Albion" and "Lubellion" would typically bridge into the powerful boss monster of Branded Despia, "Mirrorjade the Iceblade Dragon", whose effects can dump copies of "Albion" to search more "Branded" cards, completing the Deck's resource loop.
Three "Despia" Main Deck monsters provide Branded Despia with advantage-generating Fusion Materials. They each have Trigger Effects that generate advantage when they're sent to the GY or banished as a Fusion Material for a Fusion Summon.
These monsters' effects compensate for Fusion costs if they were used as materials from the hand or field. However, if they were used as materials from the Deck (only possible with the effect of "Tragedy") or GY, then they will actually generate additional advantage.
By triggering these effects on the opponent's turn with Spell Speed 2, GY-utilizing "Branded" Fusion cards like "Branded in Red" or "Branded Banishment", and by summoning Fusion Monsters with disruptive effects like "Guardian Chimera", the Deck can rapidly generate advantage in the opponent's turn, making it easier to finish the game on the player's next turn.