Whats your favorite Single Shot for offhand shooting. Does not have to be the most accurrate just the gun you like to take to the range.

My 1885 Winchester HighWalls with skeletonized hammers, coil springs, and free floated barrels were great for offhand.

They fit well, were well balanced, had good triggers and with modifications their slightly lower lock time was of no concern.

Worst single shot for offhand is the BSA Martini with the prone stock. 
Cannot get a decent hold and let off with it even though they are accurate and have good triggers.

About 6 years ago, I decided to use the only purpose built OH rifles I have and shoot all my OH with them now. 

If lock time ever becomes a issue for me, I may have to use a different rifle

Frank

230 point offhand scores aren't due to the rifle.

My favorite is my Schoyen Ballard in .38-55 for offhand. Not the prettiest gun I own, but the best shooting CF I own. 

Top gun in this image:

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For .22 I like this Bill Crane built Stevens 44.  I call it a 44-1/4 since it had a removable trigger assembly like a 44 -1/2 and an adjustable trigger.  I picked this up from Chuck Bordman when he first started selling his rifles.  Chuck spent the rest of the match showing it off to everyone.  I think he had serious sellers remorse.  

Jack

The schuetzen style rifles are really a huge advantage offhand.

One year I took one of my CPA 52's up to our local silhouette match to compare it against my Shiloh #3 in .40-65.   I'd never shot the CPA at chickens before.   The aperture sighted CPA, in .32-40 shooting black powder, was much better than the Shiloh at hitting chickens.   

At 200m my Shiloh is more accurate than the CPA shooting black powder, but the CPA #52 (with palm rest) holds so steady that hitting chickens was almost too easy.      

Chris.

My favorite offhand rifle is my 33-47 DST pistol grip Ballard.  Ballard DST for .22 also. I have shot over 230 a few times with them, but unfortunately it is not a habit 

I used to shoot nearly all my offhand iron sights back when I could see them,  I used to shoot .22 silhouette with a low wall iron sights.  White targets didn't bother me then, but after cataract surgery, that was the end of white targets if the sun came out. 

I used to shoot my BSA Martini offhand with a 36x scope.  I found it just as good or maybe a 1/2 point better per shot than my Ballard, but I have a schuetzen butt plate for it.  Without it, offhand is quite difficult with that prone shock as Schuetzendave says.