Tips for digging out a fence post

I’m terrible for using huge amounts of concrete for fixing fence posts but I’ve hit on a method of replacing them without having to remove them. 
I drill out the old stump using cheap flat wood bits then a crowbar and old chisel to get in the corners. Use the same size post as the original but reduce its size  at the base slightly, especially the corners using a flap wheel. Treat it well with preservative then some gravel in the bottom of the hole for drainage and slot in. 
Another thirty years and no digging!!

Hope this helps..

@wheelsonfire1 that sounds like a perfect solution but I fear that the reality of it might be a while load of work and I then can't get the new post in! I guess that in my favour the existing post is so rotten it should come apart easily, but I don't know if the original post is in concrete or was in soil.

fyi cheap but not nasty post Angle fix to deal with ok post rotted at ground level Get two bits of decent angle iron (old metal bed frames used to be ideal, racking  sides etc etc nowadays) , 2ft long or more, at least 2 inches wide on each side, if you can sharpen one end that helps, hammer down diagonally opposite sides of the post as far as you can (leave 9” or more out), drill holes in angle , screw to post with long screws. 

If digging out/replacing get the pre tarred/bitumen wrapped base posts as they last a bit longer at ground level.

digging out is better with a digging bar to minimise hole size and can break concrete and use blunt end to compress loose earth. 

liking the idea above of just post removal, 

ps have you checked deeds to see whose fence it is. 

@qwerty If the posts are in concrete then I have used the above method many times. We installed fencing over 35 years ago and the tanalised timber is failing in a few places. Yes it’s a bit of effort on your knees in the mud but if you take your time rounding the corners and reducing the new post base size slightly so it slots in it’s very satisfying.

I used an angle grinder and coarse flap wheel but the same could be achieved, but slower, with a rasp or a sander.

What I've done in the past is remove everything then break up the old concrete and reuse it in the cement as aggregate. Works pretty well.

Id do as Kormoran suggests.

Usually SDS drill or breaker on hammer only with a chisel bit. If you're lucky and it was postcrete, it breaks up fairly easily as it's not a strong concrete. Then obviously postcrete for the replacement. I'd attach panels ( one or both) to the post before concreting in. then it's in the exact right place and you only have to worry about verticality in one plane.

Try not to make the hole any bigger as you work.

Or remove the old post and use a cast in post base in the old post hole. Like this one:

https://www.toolstation.com/cast-in-post-shoe/p64644

The fences are "party structures" I'm surrounded by 8 other gardens with an interesting selection of fence post decay..... they've been in situ for decades and the rota probably above ground too

I've done the 'remove post from concrete and put a new post in the hole' method, and it's lasted 10 years so far 👍

After all the helpful comments I can add some what not to do!

Don't do it on a still day in the highlands where it's unseasonably warm and the midges are the size of a small bee. Digging out a corner post placed just into the soil but very deeply and getting eaten alive. So bad I tried to light a small smoky fire to keep the midges off and proceeded to cough choke and itch at the same time as sweating profusely. Yeah, don't do that.