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Hall, 32, who said he believed in a white breakaway nation, ran for a seat on the local water board in 2010 in a move that disturbed many residents in the recession-battered suburbs southeast of Los Angeles. The day before his death, he held a meeting of the neo-Nazi group at his home.

Last year, the boy — the oldest of Hall’s five children — told investigators he went downstairs and shot his father before returning upstairs and hiding the gun under his bed, according to court documents. He told authorities he thought his father was going to leave his stepmother and he didn’t want the family to split up, Mr. Soccio said previously.

The boy’s stepmother told authorities that Hall had hit, kicked and yelled at his son for being too loud or getting in the way. Hall and the boy’s biological mother previously slugged through a divorce and custody dispute in which each had accused the other of child abuse.

Kathleen M. Heide, a professor at the University of South Florida in Tampa who wrote “Why Kids Kill Parents,” said children 10 and under rarely kill their parents and that only 16 such cases were documented between 1996 and 2007. Ms. Heide also said parenting and home life undoubtedly would play a role in the case.

“It would be inaccurate to say who the child’s parents are is superfluous,” she said. “That is going to have an effect on how the child grows up, on the values that child learns, on problem-solving abilities, so all of that is relevant.”

If a judge finds that the boy murdered Hall, the child could be held in state custody until he is 23 years old, said Bill Sessa, spokesman for California’s Department of Corrections and Rehabilitation.

The state currently houses fewer than 900 juveniles.

“We don’t have anybody that young,” Mr. Sessa said. “We have had 12-year-olds in the past, but it’s rare.”