So... is Itsudatte My Santa! finished or not?
It is a bit ambiguous in this case.
Why?
The anime finished after the manga:
Anime finished: December 07, 2005
Manga finished: December 24, 1997
... But we could not confirm the source content in MangaUpdates.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
The story revolves around a perpetually unlucky young man named Santa, who has become disillusioned with Christmas due to his unfortunate circumstances.
On Christmas Eve, his life takes an unexpected turn when Mai, a spirited and enthusiastic Santa-in-training, suddenly appears before him.
Mai's mission is to bring happiness to Santa, not by delivering presents in the traditional sense, but by attempting to alleviate his loneliness and change his pessimistic outlook on the holiday season.
The anime follows their interactions as Mai strives to fulfill her Santa duties and bring joy into Santa's life, focusing on the challenges she faces in trying to connect with someone so deeply entrenched in negativity.