Where to begin?
When wood dries out it shrinks. A little bit along the length, a fair bit radially (so almost shrinking in across the grain to the centre) and a lot circumferentially (is this even a word?) (shrinking around the grain). The first two aren't a big problem, but the last one is a huge problem - the wood effectively tears itself apart because the outer layers of wood want to shrink, but the very centre can't shrink. It will usually tear itself apart in several places and possibly as far as the centre.
There are two things you can do to minimise this:
1) In small diameter wood, leave the bark on and apply some sort of sealer to the ends. You can use old paint, PVA woodworking glue or melted paraffin wax amongst other things. This slows down the drying, and hopefully avoids splits. You might also want to leave the pieces as long as possible - you might get splits at the ends, but just cut them off as and when you want to use the wood.
2) In large diameter wood you might need to pre-empt the splitting. Split the wood into halves or, probably better, quarters through the centre pith of the log. Then trim away the centre pith and the first couple of growth rings. Doing this will allow the wood to shrink as it's going to do anyway but should minimise or avoid stresses building up in the log and the log tearing itself apart.
I was checking out two halves of a log of Scots Pine yesterday. The centre pith was a bit offset, and the half log without the centre pith has dried out nicely. The half log with the pith has split down to the centre pith, almost giving me two quarter logs.
I realise that this means that you will end up with smaller peices of wood, but hopefully the wood ends up being split free.
Oak and ash will probably dry slowly without issues, but birch can be a real pig for rotting if it stays wet for too long. If you are intending carving the birch, I'd carve it green and then dry it (carefully!). See
post 15 here.
Cheers