I need to make an eggless birthday cake for tiny person's party as one of the kids has an egg allergy, and I'm not an arsehole, so we're making one cake that's inclusive.

Today I'm experimenting with the Bobs Red Mill egg replacer, but it made the cake batter ridiculously thick (yes, I followed instructions). So thick it didn't have a hope of rising. So, I added about 1/2 a cup of milk until it could be spread in the pan without effort (it was thick...). Put it in the oven, but I'm not that hopeful right now... I think I'm going to end up with bricks.

Would appreciate some links to some tried and tested egg-free cakes. I've got a week to crack this.

@Teaceratops

Not a link, it looks like you're using rounds but this is usually done in a 9x13 cake pan, so maybe halve it if you're using an 8" round?

Combine in your cake pan (important):
3c flour
1 tsp salt
1/2 cup cocoa powder
2 tsp baking soda
2c sugar

Make three little divots in your mixture, and placed one of each in a divot:
3/4c oil
2 tsp vanilla extract
2 tbs vinegar

Pour 2cups of water over it all, and stir well.

Bake at 350 F for 20-30 minutes, until a toothpick comes out clean