In addition to a letter giving permission by the absent parent, my ExH, I also discovered recently that that letter has to be notarised at a police station, along with a copy of the absent parent's passport.
Also, you need the child's birth certificate, with both parents names included and a copy of your passport to attach to them.
I discovered this at the check in, attempting to go to South Africa. Great fun.
When he dies, I will need a copy of his death certificate, until my youngest is 18.
If we were NC, then the trip would have been cancelled - I have no idea if I would have got my money back. As it is, it took four days to get the paperwork together and the airline graciously changed our flights, free of charge. Perhaps they felt they should have made it clear when the tickets were booked?
I had the same issues going to Nigeria, several years back - but at least I knew about it then as we had to get visas in advance.
I'll never take the risk again, wherever I go with the kids. I aged ten fecking years!