I can not find this manga at all.... A girl gets a heart transplant and gets powers from the heart. Guy appears to protect her from the darkness. Lot's of monsters and some people try to kill her as she learns to be a miku...

Does this sound familiar to anyone?

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It's not exactly what you're looking for, but in the final arc of Jiraishin, the story revolves around the heart transplant from a dead woman to another woman, and the woman who receives it is actually an assasin, but after the heart transplant she is plagued by the feelings of the owner of the heart which carried on over to the assasin, and she can no longer do the jobs that she is hired to do.

No there's a series I read a while ago that was all about it. She gets the heart in the beginning and then the guy shows up in the hospital[i think] to save her from people after her new power.

There was an arc that had people loyal to the old owner of the heart that used black magic to raise her from the dead. She goes crazy and the new owner has to stop her... Bodyguard is in love with both owners.

There was a fight with a youki at Mt. Fuji... some twins folktale...

Any of this ringing a bell?

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maybe Eien Kamoshirenai?
(didnt read it myself, just sounded similiar based on the description...)

[Edit]
maybe not, just reread the description and it doesnt mention a heart... dont know how I read heart in there :x

That's it.... thanks!

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Oh... so its it after all, well, youre welcome