what rights does surviving children have on a deceasedparents estate when a step parent is envolved and there is no will in Louisiana?

Louisiana is a community property state.  Property is divided up into separate property (that which is brought into the marriage, or inherited, or awarded in a personal injury settlement), and community property (that which is earned during the marriage, including a house purchased with community assets, retirement benefits, employment income, etc.)  Without a will, the spouse gets half of the community property and the right to use the other half until death or remarriage.  Then the remaining one-half goes to the children.  The separate property goes to the children.