So... is Vampire Holmes finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Vampire Holmes presents a comedic take on the legendary Sherlock Holmes. This version of Holmes and his assistant, Hudson, are supposedly vampire hunters hired by the London police.
However, the reality is far less glamorous. Instead of solving crimes, they bicker, loaf around, and generally fail to live up to the image of brilliant detectives.
Adding to the chaos is a demon cat named Kira and their frightening landlady, making their everyday lives far from ordinary. It's a story about a detective agency that is anything but successful, and a Holmes who is definitely not London's greatest.