Warning: TL;DR incoming. When I post, I rant.
I should probably be upfront that I do not have any tulpas, and I am not currently tulpaforcing though the idea intrigues me (very new to the concept and far too aware of the ethical implications and responsibilities of creating a sentient intelligence to just jump straight in). Not the thread to talk about that so I won't say more, but I thought I'd be upfront about that so that anyone reading this knows that my descriptions of these "tulpa analogues" and "how tulpa-like" they are is not based on firsthand knowledge.
That said, let's begin. I only have a few, but I think are least some of them have not been mentioned yet (and the ones that were I didn't notice more than brief sentences about and I prefer more long winded explanations, as should be painfully obvious to you by now). A lot of these are fanfiction and may contain unmarked spoilers for the series they are based off of. Mostly because talking about at least some of them while marking all of the spoilers for their parent series would basically necessitate making their entire entry spoiler marked. Instead I will inform you on if they are fanfiction, and of what series, before describing them. I will try to avoid spoiling the fanfic itself, though, because that should be easier to do.
I feel these stories get something pretty close to what is described as a tulpa here on the boards, even if it obviously isn't the original intent.
"Time Braid" (fanfic)
(Naruto, though it is so lightly present, doesn't spoil its source material in any way I can think of, and still manages be a massive spoiler for the fic that I recommend you not mouse over it if you want to avoid such spoilers)
One of the most unique things about this fanfic that made me love it was the seeming drastically different usage of one of its plot elements, which in retrospect resembles tulpas immensely. The fic is not about tulpas necessarily, the story's main focus is on a time loop plot (for those unfamiliar with the concept, think/look up Groundhog Day or the recent movie Edge of Tomorrow). However, the plot element that involves something similar to tulpas is heavily present, as it was probably a useful tool to give the looping protagonist something to focus on beyond eventually overpowering everything in the universe (as these stories almost necessarily devolve into in fanfic).
The story focuses on Sakura as she one day discovers that every time she dies, or fails the Chunin exam, she wakes back up in her room on the morning of the exam. Frequent Naruto fanfiction readers will likely recognize this as very reminiscent of the relatively (in)famous fic Chunin Exam Day, which the author acknowledges and quite possibly wrote this as a response towards. I personally find this to be the better of the two stories.
The tulpa elements come in with how the fic handles the concept of "Inner Sakura." For those not in the know (apparently you are reading this and yet somehow never read and never care to read Naruto... and still want to see a discussion of a Naruto fanfic?), Inner Sakura is a device used by the author of Naruto (Masashi Kishimoto) to show Sakura's inner thoughts. Sakura as a character could be described as some kind of variation on a tsundere, although unlike most characters of this type she focuses her affectionate side on one character (Sasuke) and her angry side on another (Naruto). She tends to take the sweeter side as her default persona towards people at large (though not to the same extent as she does with Sasuke, who she has a crush on). Inner Sakura is used by Kishimoto to show us what Sakura is really thinking during these moments of cognitive dissonance, and ironically shows her to often agree enthusiastically with the more blunt Naruto despite being something she never admits out loud.
Inner Sakura, as portrayed canonically, is probably not a tulpa. She is designed purely to show the viewpoint of Sakura's real opinions, and is thus not something separate from herself. There is one incident where the existence of Inner Sakura causes extreme peril to a mind reader/controller. This is, however, the only time it's used as anything but a narrative device, and could easily be interpreted as Sakura just overcoming the mind powers through mental strength, especially since said victim never mentions it again. Later into the story, as Sakura becomes more confident and starts saying what she means more often (in other words, when the dissonance fades) Inner Sakura disappears, which if interpreted as a tulpa would be somewhere between sad and horrifying.
Time Braid is not the canon.
In Time Braid the concept of Inner Sakura is explored as if she were some kind of separate consciousness. This is fairly common in Naruto fanfiction, where writers for various (sometimes mean spirited, sometimes not) reasons often deconstruct this plot device as some form of dissociative disorder. These do not qualify in my mind as "Tulpa Like" (at least in not in any way I find interesting) because it is being treated as a sickness. Time Braid hints at this idea very early on, in the very first chapter Sakura encounters difficulties getting people to believe her about the time loops and at one point it is mentioned that in at least one early iteration she spent time in a mental hospital, where they examined the possibility that she has some kind of DID-like disease.
However, the fic does not ultimately treat this as a disorder for Sakura. Instead A good deal more such are constructed in her mind as the fic goes on, under various circumstances. Usually this involves some intense mental effort on Sakura's part, especially early on, which could be very analogous to tulpaforcing. It isn't a flawless analogy, since it generally happens far faster than most hosts would probably reasonably expect, but it is a reasonable comparison. During the scenes where Sakura identifies and comes to terms with what this process means, and how it works, she does consider the idea that it might be an illness, but ultimately comes to the conclusion that it is not. This is probably a mindset many hosts might have gone through at some point, the ever common question of "Is this real? Am I going to damage myself if I do this?"
Ultimately once Sakura identifies how Inner Sakura and other "tulpa-analogues" work, they serve multiple functions that are similar to the tulpa in a real host. Given Sakura is effectively isolated form other humans by the timeloops, these personalities give her some form of companionship at times in the story. They also serve to help Sakura understand how her mind works a lot better, and help her with everyday tasks quite often (though admittedly, often in ways that could very well be impossible in real life).
The "tulpas" are almost never portrayed as negative. They might have some conflicts, like you might with a real tulpa, but they're practically never shown to be malicious of their own volition. So ultimately all of that spoilered voodoo probably just reinforces the idea of tulpas as a coping mechanism, depending on how you choose to see it.
Like real life tulpas, these analogues are not shown to be able to affect the world outside Sakura's head on their own (again, if I remember this right, it has been a year since I read this). This comes with the pretty huge caveat that the world of Naruto comes prebuilt with magic ("Jutsus" using "chakra") as a reproducible phenomenon. Including creating copies of yourself (right down to it have the same brain you do and sharing memories), and a technique that allows you to change your appearance. Yeah, this is absolutely used to allow the analogues to interact with the real world in a way much more mystical than what most would want to consider in real life. You could count this as a negative point on how tulpas are portrayed (as in "negatively impacts how realistic it is"), but I don't because the magic used to do this is not particularly a power the tulpa itself gives Sakura. Plus magic, you know, actually exists for characters other than the "tulpamancer" in this universe, which personally makes me see it as a wash.
Unfortunately, less forgivable of a "negative points" scenario is
Unfortunately, other aspects of the mechanics of it all are possibly even worse.
Then there comes (part of) the explanation of the relevance of the spoiler in the list of universes that are used in the fic.
Ultimately I feel Time Braid contains by far one of the closest analogues to the tulpa phenomena. You have to be willing to accept quite a few caveats, but most of these are pretty minor. It does make it a matter of interpretation though. I have more but this post is already super massive, so… I’ll save them for another time.