There isn't much conflict between us anymore, so when an expense that we are supposed to split comes up, we'll send a text to eachother detailing it, as well as a picture of the receipt. Generally an E-transfer is sent that day for half the amount. On the rare occasion it's a higher value amount, I'll usually end up paying the full amount, and collect her share from her over a few pay periods.
Wouldn't likely work very well operating like that for people still involved in court, or for high conflict types.