Section 3044 is the strongest presumption in California custody law. Subdivision (a) provides that on a finding that a party seeking custody has perpetrated domestic violence within the previous five years against the other party seeking custody, against the child or the child's siblings, or against a person described in § 3011(a)(2)(A) with whom the party has a relationship, there is a rebuttable presumption that awarding sole or joint physical or legal custody to that person is detrimental to the best interest of the child. The presumption may be rebutted only by a preponderance of the evidence.
Subdivision (b) sets out how it is overcome, and it is demanding. The court must find both that the perpetrator has demonstrated that giving them sole or joint custody is in the child's best interest under §§ 3011 and 3020, and that a list of additional factors on balance supports the legislative findings in § 3020. Critically, the preference for frequent and continuing contact with both parents in § 3020(b), and the corresponding language in § 3040(a)(1), may not be used to rebut the presumption in whole or in part — the usual argument for contact is expressly taken away. The additional factors include successful completion of a batterer's treatment program meeting the Penal Code criteria, of alcohol or drug abuse counselling where appropriate, and of a parenting class where appropriate; compliance with probation or parole; and compliance with any protective or restraining order.
What triggers the presumption is a finding by the court of perpetration of domestic violence within five years, which does not require a criminal conviction. This is a technical area where the sequence of findings matters a great deal, and it is one where a family lawyer, and where relevant a domestic violence advocate, should be involved rather than the statute read alone.