There was a 2004 comic con exclusive one that came with a real leather coat and a pewter Samaritan. I have that one. It's the best made coat I've ever seen for a figure that size.
You'd have to buy the figure over again though to get it, unless you can find someone selling it loose.
His fist is polystone though so it's worth it.
I just avoided the whole which has the trench which doesn't thing and bought comic style from Mezco with the trench, I like him better than the movie figs.
I got this hellboy when the first movie came out that came without a shirt, had a cigar in his mouth, had an open stone hand and came with a dumbbell. He also came the bada$$ soft trenchcoat that you could put on any HB figure that did not have on a trench already. Currently, my hellboy with the black shirt is wearing the trench. It is one of the best accessories for HB that Mezco made.
If you look at this pic, you can see the trench behind the figure. I checked out Ebay and did not see a listing for this figure so it may be hard for you to find him now. Good luck. I really liked the figure and the coat. They are the best of my collection in my opinion.
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You could probably get the Hellboy trench that was made for the Animated figure but it may look a little bulky on the Movie figure.
I know they made a Hellboy from that first movie line with a molded movie coat. As far as the new movie Hellboy that came out with the animated figures, there was no coat.