Mel Gibson and his ex-girlfriend Oksana Grigorieva are battling over which Californian school their daughter, Lucia, will attend.
The former couple are in disagreement over where their 21-month-old daughter Lucia will be educated, with Oksana wanting to her to be enrolled near her home in the San Fernando Valley, which Mel objects to as it is over 40 miles away from Malibu, where he lives.
Mel wants Lucia to attend another school halfway between their homes, which would make it more viable for him to pick her up and drop her off.
The custody case is being fought in closed court, but sources tell gossip website TMZ that Mel wants a 50/50 custody arrangement, which he believes would solve most of the issues between him and Oksana - whom he split from in June 2010 - although she is thought to be opposed to his proposal.
Oksana is said to still be so bitter, she would rather have a long and expensive court case rather than reach a settlement out of court.
Earlier this year, Mel agreed to plead no contest to simple battery relating to an argument he had with Russian-born Oksana in January 2010, a lesser charge than corporal injury on a spouse, which he was originally facing.
While Mel - who has seven other children with his ex-wife Robyn - felt he was in a strong position to win, his lawyer, Blair Berk, said he accepted the plea to escape a long court fight.
He said in a statement: "I know from almost 20 years as a criminal defence lawyer that sometimes Justice can come for a client at too high a personal price.
"Mel's priority through all of this has been that the best interests of his young daughter Lucia and the rest of his children be put first in any decisions made. It is with only that in mind that he asked me to approach the District Attorney with a proposal that would bring all of this to an immediate end."