Gabriel Aubry is asking the judge in his custody war with Halle Berry for a half a million bucks in attorney's fees, and $20,000 a month in child support, TMZ has learned.

Gabriel was in court this morning, expecting to argue his case for the huge increase in child support, but the case was continued because the paperwork wasn't filled out properly.  Gabriel was extremely upset the matter was put off.

Sources tell us ... Gabriel believes he's entitled to the money because he needs a proper environment to care for 4-year-old Nahla. 

As we first reported, Halle wants to move with the child to Paris, which would have a direct impact on Gabriel's request for additional support.

Halle Berry is banking on her custody judge giving her the green light to move to Paris with 4-year-old Nahla -- because we got pics of her checking out preschools in Paris.

TMZ broke the story ... Halle wants to move to France with her fiance Olivier Martinez and Nahla to escape the paparazzi that dogs her in the states.  She also feels unsafe in the U.S. because of ongoing stalker issues and fears for Nahla's safety.

Baby daddy Gabriel Aubry is fighting the move, claiming it's bad for Nahla to sever meaningful contact with him.

The judge has yet to rule on the move.

The dependency court case against Gabriel Aubry has been dropped ... sources connected with the matter tell TMZ.

As TMZ first reported, Gabriel was in court today as the judge wanted to discuss various conditions for his visitation rights with 3-year-old Nahla.  Parents are sent to dependency court when there are concerns over the well-being of their children.

Gabriel was hauled into court after the L.A. County Department of Children and Family Services expressed concerns about the child's safety in the presence of Gabriel.

We're told additional conditions were imposed on Gabriel's visitation, and the matter has now been dropped and sent back to family court, where Halle Berry and Gabriel continue to fight over custody.

Gabriel Aubry just showed up at dependency court in L.A. where a judge will decide if even more restrictions will be placed on his custodial rights.

Sources tell us the judge is expected to lay down a series of orders ... requiring Gabriel to do various things to ensure the safety of 3-year-old Nahla.  The judge will hear from the social worker on the case as well as the attorney appointed to protect Nahla's rights. 

As TMZ first reported Gabriel was hauled into dependency court following a child endangerment investigation. Gabriel can only visit with Nahla in the presence of a court monitor and the judge has imposed other restrictions as well.

What's especially significant ... once the judge establishes the ground rules for Gabriel's visitation rights, the case will go back to family court where Halle is trying to convince the judge to allow her to move to France with the child.

TMZ broke the story ... Halle wants to move out of the country because of the problems she's having here with paparazzi and stalkers.

Gabriel Aubry wants his 3-year-old daughter Nahla to live in surroundings to which she has become accustomed ... and he wants Halle to pay dearly for it.

TMZ has learned what Gabriel wants in the way of $$$ -- and it's a lot.  We've learned Aubry has filed legal docs asking the family law judge to force Halle to give him $15,000 - $20,000 a month for a proper home. 

Gabriel has also asked for a laundry list of other things from Halle, including what we're told is a "very large" amount of money for the little girl's clothing, as well as money to take the child to Canada to visit his family.

We're told Halle is fighting Gabriel tooth and nail on his request. The hearing on the money issues was scheduled for Monday, but it's now been put off until April 9, in part because the family law judge wants to see what the dependency judge does to Gabriel. 

If the dependency judge takes away some of Gabriel's custody rights, it would have an impact on any child support Halle would have to fork over.

Halle Berry has dumped another man ... but this one has been with her way longer than all the others -- her longtime lawyer/confidante, Neal Hersh ... TMZ has learned.

Here's the lowdown. Our sources tell us Halle wants to go after her baby daddy Gabriel Aubry with nuclear weapons -- metaphorically speaking -- and she thinks Hersh is too much of a gentleman to wage that kind of legal war, even though he has guided Halle through 2 divorces, a custody war and various other legal skirmishes.

So we've learned Halle has hired Stephen Kolodny (above), who is legendary in L.A. legal circles for the level of legal warfare she so wants. You may recall Kolodny repped Mel Gibson in his epic battle with Oksana Grigorieva -- and that got kinda nasty.

Kolodny has already gone to court with Halle. We've learned last Thursday the new duo went to dependency court to have more restrictions placed on Aubry. The dependency judge has already ordered that Gabriel can only have contact with Nahla in the presence of a monitor. On Thursday, we're told the judge voiced additional concerns and ordered Gabriel to return the child to Halle earlier than the 6 PM deadline on days he has custody.

Kolodny will have his hands full trying to convince the family law judge that Halle should be able to move to France with the child because she's concerned about paparazzi and safety. 

One thing's for sure ... it's gonna get nasty.

Hersh and Kolodny could not be reached for comment.

Halle Berry's baby daddy Gabriel Aubry will not be charged after allegedly shoving his daughter Nahla's nanny ... while the woman held Nahla in her arms -- TMZ has learned.

TMZ broke the story ... Gabriel flew off the handle last month when the nanny questioned him about not taking Nahla to school one day. According to the battery report, the nanny picked Nahla up during the confrontation, and Gabriel allegedly shoved her out the door with Nahla still in her arms.

But L.A. City Attorney spokesman Frank Mateljan tells TMZ ... Gabriel will NOT be charged because of "insufficient evidence."

Gabriel isn't completely off the hook -- as TMZ previously reported, a Dependency Court judge placed an order stating Aubry can only watch Nahla while under the supervision of a monitor ... per a recommendation by the L.A. County Department of Children and Family Services.

Halle Berry's fiance Olivier Martinez proved he's strong enough to carry the family ... or at least Nahla ... during a fancy dinner date in Malibu this weekend.

After hearing the good news about Halle's stalker being re-captured by authorities, the gang hit up Nobu Saturday night.

Nahla looked pretty comfortable with Olivier ... tightly embracing the guy as he carried her out to the car.

As TMZ first reported, Nahla has issues with the other man in her life ... her father Gabriel Aubry ... telling the L.A. Department of Children and Family Services she's scared of him. Gabriel is now only allowed to see Nahla with a monitor present.

Sources tell us the L.A. Department of Children and Family Services conducted numerous interviews with people familiar with the relationship between Gabriel, Halle Berry and Nahla. We're told DCFS now has numerous incidents that have raised concerns about Gabriel’s ability to properly parent his child.

We're told DCFS conducted an interview with Nahla, who talked about her father and described incidents involving him screaming at her -- and how it made her extremely frightened.

Our sources say DCFS has information about Gabriel  yanking the child out of the nanny’s hands, allegedly pushing the nanny while holding the child, and putting the child in harm’s way while Halle was shooting a movie in Europe.

As TMZ previously reported, the Dependency Court ordered that Gabriel can only have contact with his daughter in the presence of a monitor to ensure the safety of Nahla. But we're told that is just the beginning ... there will be numerous other hearings, as well as additional requirements that Gabriel must fulfill, which will include various forms of counseling.

As we reported earlier, Gabriel agreed to anger management counseling ... but we're told the Dependency Court will order more than that.

Just a note ... Dependency Court is different from the family court where Gabriel and Halle have been frequent visitors over the past year. Dependency Court is designed specifically to protect a child when there are signs of neglect or abuse. Being hauled into Dependency Court is far more serious than a family law skirmish.

Gabriel Aubry is being watched ... watched by a monitor whenever he's with Nahla ... 'cause a judge ruled he can't be trusted with the child alone, at least for now.

TMZ broke the story ... Halle Berry's baby daddy was ordered into Dependency Court today after the L.A. Department of Children and Family Services concluded its investigation. As we reported, DCFS not only looked at an incident in which Gabriel allegedly pushed a nanny while she was holding Nahla, but other incidents as well.

We're told DCFS had information that Gabriel had yanked the baby from the nanny's arms on at least one occasion and screamed at Nahla multiple times.

We're told DCFS had extensive information that it had reviewed and then recommended a monitor for Gabriel when he has Nahla.

We're told .. the judge agreed this morning and put the monitor in place after a hearing.

Gabriel Aubry has been orderd to appear in Dependency Court because authorities are concerned about his ability to safely care for his child ... TMZ has learned.

Aubry is in court right now and the appearance was triggered by the L.A. County Dept. of Children and Family Services' investigation into allegations that Aubry is guilty of child endangerment.

Sources tell TMZ ... the DCFS investigation goes beyond an incident in which Gabriel allegedly pushed the nanny who was holding 3-year-old Nahla.

We're told DCFS is concerned about Nahla's safety in the care of Gabriel and that is why he was ordered to appear in Dependency Court.

We're told no ruling has been handed down ... yet.


10:48 AM PST -- TMZ has learned ... Nahla now has legal counsel that has been appointed by the court to represent her in the hearing.