Anima Visage
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Best users are Garen, Illaoi, Scar and Vander. Mundo and Elise often receive the item, but don't perform as well with it.
Anima Visage is mainly used an additional frontline item.
Blighting Jewel
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Best users are Morgana in early game and Malzahar in late game. Heimerdinger, Silco and Ekko can also make use of the item to an extent, as they have multiple instances of magic damage. Rumble is a good lategame option once you find Junker King Upgrades, especially Flamethrower.
Blighting Jewel can also be surprisingly strong on tanky Frontline units with the Anomaly "Thornskin". It reflects a lot of magic damage without cooldown, making it perfect to reduce the MR of the enemy frontline to 0.
Blighting Jewel is best in slot for Hero Singed.
Death's Defiance
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Best users are Camille, Violet, Smeech and Sevika. Ambessa, Vi and Mordekaiser can also make use of the effect. Death's Defiance mainly acts as a stronger alternative to Bloodthirster or other sustain items.
You can make use of the self inflicting damage to stack your own Titan's Resolve faster.
Deathfire Grasp
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Best users are Malzahar, Leblanc, Ekko and Powder. Heimerdinger and Silco can also take it as an alternative AP item.
Works well together with Ionic Spark to chunk enemy tank at start of the fight and can be surprisingly useful to help deal with the Monster Crab in Crab Rave Encounter.
Fishbones
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Best users are Draven, Jinx, Nocturne and Mordekaiser.
Units like Corki, Tristana and Lux can also potentially snipe down the enemy carry with Fishbones, as they have very high single target burst. Fishbones works great with other range increase effects.
Gambler's Blade
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Best users are Kog'Maw > Zeri in early game and transfer to Malzahar/Leblanc in late game.
Gambler's Blade is a popular choice from the Augment "All That Shimmers" in Stage 2-1. Most commonly used in Kog'Maw reroll as he does nothing except attack with high Attack speed resulting in a lot of gold.
Gold Collector
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Best users are Jinx, Camille, Twitch, Corki, Draven and Smeech.
Gold Collector is a popular choice from the Augment "All That Shimmers" in Stage 2-1. Most commonly used with a Maddie or Draven Opener and transfer to AD carry in late game.
The Execute effect does not stack with Augments like "Noxian Guillotine" or "Finisher" Anomaly. Only the highest threshold is relevant.
Horizon Focus
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Best users are Elise, Scar and Vi.
Has synergy with Anomalies like Diving In, Dramatic Entrance and Unstoppable Force. Also works well with the Support item Spite and other Artifacts like Silvermere Dawn.
Hullcrusher
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Best users are Elise, Illaoi, Mundo, Vi or Scar.
Hullcrusher is a fairly generic frontline Artifact. It has negative synergy with Augments like Bulky Buddies or Anomalies like Hungry for Power.
Infinity Force
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Best users for Infinity Force are Camille, Smeech, Violet, Ekko and Sevika.
While the item looks generic, it grants a surprisingly high amount (+25) of mana. This makes it valuable for some units that want to cast very early like Caitlyn or Sevika.
Innervating Locket
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Best users for Innervating Locket are Garen, Illaoi, Scar, Elise and Vander.
It has good synergy with Anomalies like Giant-Sized, Fortified, Dramatic Entrance or Legacy of Shurima.
Lich Bane
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Best users for Lich Bane are Kog'Maw and Visionaries like Heimerdinger or Malzahar. Can also give it to Zoe or Leblanc in late game as an additional AP item.
Lightshield Crest
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Best users for Lightshield Crest are Garen, Illaoi, Elise, Vander, Loris and Scar.
Has positive synergy with Sentinel trait, Stoneplate and Anomalies like Stoneskin.
Luden's Tempest
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Best users for Luden's are Powder, Lux, Ekko, Jinx and Caitlyn.
You want Luden's on units with high single target damage, if you give it to to someone like Heimer you will barely receive ony overkill damage since it will only count a single rocket. Can be good item for Tristana in the right setup.
Manazane
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Best users for Manazane are Visionaries like Heimerdinger/Malzahar or Dominators like Silco/Ziggs. Jinx is also quite strong with it, since she will cast her rocket quite fast.
Mittens
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Best users for Mittens are Violet, Smeech, Mordekasier, Camile and Sevika. It'sa strong item on any Melee carry that makes use of the high Attack speed.
Mittens is also the best Artifact for Hero Singed, as he makes very good use out of the bonus Movementspeed.
Mogul's Mail
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Best users for Mogul's are tanky Frontliners like Scar, Garen, Illaoi, Elise or Vander.
Prowler's Claw
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Best users for Prowler's Claw are usually Ambushers like Camille or Smeech and strong Pitfighters like Violet and Sevika.
Prowler's has positive synergy with Firelight Augment Aerial Warfare.
Rapidfire Cannon
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Best users for Rapidfire Cannon are Mordekaiser, Nocturne and Draven. Jinx can use the high AS to generate mana and Sevika's Flamethrower has positive synergy with range increase.
Works well with Eagle Eye Anomaly, that increases AD if unit stands still.
Seeker's Armguard
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Best users for Seeker's Armguard are Ekko, Mordekaiser, Rumble and Malzahar.
Silvermere Dawn
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Best users for Silvermere Dawn are Camille, Violet, Sevika, Smeech and Caitlyn.
Good for Maddie Reroll with Cosmic Insight (disabled in patch 14.24).
Sniper's Focus
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Best users for Sniper's Focus are Jinx, Mordekaiser, Draven, Nocturne and Sevika. It's quite similar in concept to RFC, but it has more alternative users like Malzahar or Sniper units.
Spectral Cutlass
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Best users for Spectral Cutlass are usually strong AD Melee carries that can snipe enemy carry and survive long enough to get teleported back.
If a unit has 2x Spectral it won't teleport at the start of combat and instead teleport after 8 seconds to the backline.
Can give Spectral to units like Darius, position him in your 3rd row and everyone else in your last row to wrap enemy team around him.
Suspicious Trench Coat
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Best users for Suspicious Trench Coat are strong AD users that also want to run Edge of Nigt. You can isolate them in the front row and split them into the enemy backline.
Coat copies don't proc Nothing Wasted mana gain, but will increase Force of Friendship damage amp, while the copies are alive.
Talisman of Ascension
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Best users for Talisman are either high HP tanks that survive long enough (with help from tank Anomalies), or backliners like Draven that can clean up the board after Vander/Violet bought enough time.
Trickster's Glass
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Best users for Trickster are Garen, Vander, Violet, Elise or Sevika. Draven and Darius are great users if they have a Family Emblem to reduce ther max mana.
Trickster Clone does not work with Nothing Wasted anomaly.
Unending Despair
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Best users for Unending Despair are Garen, Loris, Blitzcrank or Vi.
Can be decent item for Frontline in Renata Reroll.
Wit's End
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Best users for Wit's End are Kog'Maw, Mordekaiser and Ekko.
Zhonya's Paradox
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Best users for Zhonya's are Heimerdinger, Malzahar, Ekko, Mordekaiser and Rumble.