Carnival Phantasm is an adaption of the manga "Take Moon" by Type-Moon's Eri Takenashi, to celebrate Type-Moon's 10th Anniversary. 
Carnival Phantasm shows parodies and new stories loosely based on Type-Moon's original works like Melty Blood, Fate/Stay Night, Tsukihime, and more.

Takenashi Eri's comedy TYPE-MOON spoof set in the world of Tsukihime, MELTY BLOOD, and Fate/Stay Night. 
 
This manga is most famously the source-material for Carnival Phantasm.

A DVD-only episode bundled with the special edition Take Moon volume. 
Caren Ortensia attempts to control the world using money with varying degrees of success, Phantas-Moon receives a movie adaption of her T.V. show, and Shiki is involved in a love plot that spans years. 
(Source: Wikipedia)

A new episode of Carnival Phantasm released on the Type-moon Fes - 10th Anniversary Event - Blu-ray.

Shiki Tohno sustained a life threatening injury as a child, and due to that incident he was sent away from the Tohno household and was given to a relative to be raised. Years later, when Shiki is in high school, the head of the Tohno household&mdash;his father&mdash;dies, and he is ordered to move back in by his sister Akiha, who is the new head of the household. However, Shiki holds a huge secret. Ever since that injury, he has been seeing lines on objects, and only with a special pair of glasses is he able to stop seeing them. Also he is unable to remember anything well from the time before his accident. The day he moves back to the Tohno household is the day he stumbles upon a woman named Arcueid Brunstud and decapitates her with one stab of his knife in a temporary fit of insanity. When she suddenly showed up beside him later alive and well, and ask him to be her bodyguard, Shiki's journey to unravel the mysteries of his past begins.
 
(Source: Anime News Network)

Raised by a mysterious sorcerer after the death of his parents in a catastrophic fire, Shirou Emiya has only just begun to learn small tidbits of magic. When he is caught in a battle between two powerful Magi, however, he ends up performing a spell above his expected ability, accidentally summoning a beautiful woman knight to protect him. 
 
Shirou is thus unwillingly thrust into the competition known as the Holy Grail War where Seven Magi called Masters, together with their spirit partners called Servants, fight to acquire a powerful artifact said to grant every wish.

Fuyuki City - a city surrounded by the sea and mountains becomes the setting for an ancient ritual. Seven masters are given control of heroic spirits in order to realize the mythical Holy Grail, which is said to grant its owner any wish. These heroic spirits or servants represent legendary heroes of various classes: "Saber," "Lancer," "Archer," "Rider," "Caster," "Assassin," and "Berserker." Each master will enter into a contract with their chosen servant and battle the others to the death until only one pair remains... This is the "Holy Grail War." 
 
The young and capable mage, Rin Tohsaka, prepares for her long-awaited Fifth Holy Grail War to begin... With her servant Archer, Rin enters the Holy Grail War as the sole heir to the prestigious Tohsaka family after her father's death. But when Shirou Emiya, a boy from Rin's school, unwittingly becomes a Master and is fatally wounded in battle, she has no choice but to save him. With Shirou and his servant Saber, Rin sets out to strike down the conspiracies surrounding the Holy Grail War. Will the Holy Grail bless Rin and Shirou's path toward victory or will they be cursed with defeat? 
 
(Source: Aniplex of America) 
 
Notes: 
- Includes Prologue. 
- The first, second and last episodes aired with a runtime of ~48 minutes as opposed to the standard 24 minute long episode.

September, 1998: In the city where Shiki lives, something triggers a spate of mysterious schoolgirl suicides. The connection between the girls who've leapt to their deaths is unclear, although all of them have jumped from the Fujou Building, a skyscraper scheduled to be demolished.
 
(Source: Aniplex USA)

Based on the Doujin Fighting game, 'Melty Blood', made by the Doujin group, Watanabe Seisakujyo now known as French Bread. The story is one of two side-story sequels that occurs approximately a year after the good ending story of Arcueid's from the original Type-Moon game, Tsukihime. 

One year has passed since the "Serial Vampire Homicide case", that occurred in Tsukihime, was solved. But now the rumors of the serial murder are happening again and so once more Shiki Tohno patrols the city to find this phantom killer. While patrolling he meets and fights a mysterious woman by the name of Sion Eltnam Atlasia, member of the church group 'Alchemist of Atlas', who is in search of curing vampirism. But to do so she needs data from Arcueid, the last True Ancestor, to help her in her research. But this wont be easy as Ciel is also patrolling the city looking for the rumored killer, while Akiha has been acting strangely the past few days and also Arcueid hasn't been seen for awhile, could she be the killer...?

This is the adaptation of the 2nd route of the popular visual novel: Fate/Stay Night. In this route, Tohsaka Rin will be the major female character. Revelations about Shirou and his destiny will be made. 
(Source: AnimeNfo)

With the promise of granting any wish, the omnipotent Holy Grail triggered three wars in the past, each too cruel and fierce to leave a victor. In spite of that, the wealthy Einzbern family is confident that the Fourth Holy Grail War will be different; namely, with a vessel of the Holy Grail now in their grasp. Solely for this reason, the much hated "Magus Killer" Kiritsugu Emiya is hired by the Einzberns, with marriage to their only daughter Irisviel as binding contract.
 
Kiritsugu now stands at the center of a cutthroat game of survival, facing off against six other participants, each armed with an ancient familiar, and fueled by unique desires and ideals. Accompanied by his own familiar, Saber, the notorious mercenary soon finds his greatest opponent in Kirei Kotomine, a priest who seeks salvation from the emptiness within himself in pursuit of Kiritsugu.
 
Based on the light novel written by Gen Urobuchi, Fate/Zero depicts the events of the Fourth Holy Grail War—10 years prior to Fate/stay night. Witness a battle royale in which no one is guaranteed to survive.
 
(Source: MAL Rewrite)
 
Note: The first episode aired with a runtime of ~48 minutes as opposed to the standard 24 minute long episode.

Series focused on parodies and stories based on Fate/Grand Order. 

Episodes: 
1) The First Singularity Party 

As more and more Servants join Chaldea, maintaining resources for so many is becoming a problem. And so, a cruel order has been given... 

2) The Second Singularity Party 

Jeanne d’Arc Alter needs a serious amount of QP because of reasons, so she heads to the Kabukicho Singularity, the glittering gem of the nightlife scene, where she begins working at CLUB M. There, she hopes to become the best in town! However, she must first contend with a slew of troublesome customers, as well as the Four Elite hosts. 

3) The Third Singularity Party 
"The Security Organization for the Preservation of Humanity, Fenis Chaldea." 
Here, a large number of Servants gather, proudly spending their days under the command of their Master. However, the Servants face a secret problem... They are divided by a sense of inequality. Longer waits between deployment, levels never being raised...
Reality hits the Servants hard, and frustrations gradually build up. In order to correct such disparities, one Servant steps up...
 

4) The Fourth Singularity Party, MAX Bond Channel 

"I feel like Master's been more cold to me recently." 
Ereshkigal feels some distance building between herself and Master. In order to increase her appeal, Dumuzid suggests something out of the ordinary: to use a video sharing platform called "ServantTube"! Will Ereshkigal become a famous streamer and grab Master's attention?
 
(Source: Aniplex)
 
Note: 1st Season released June 2, 2021 while 2nd Season released October 13th, 2021. 
The first episode of "Season One" was pre-aired on the Fate Project New Year's Eve TV Special 2020 program.

Fate/Prototype is a digest version of Nasu's original concept for Fate/stay night.

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