California Intestate Question

My mother died last fall in California, having lived there for decades in a home with her partner, who died this spring. The house was held in both of their names and I have been told it was a joint tenant arrangement. I understand that the house belonged in full to her partner after her death.

Neither apparently had a will. The petition filed by the (future) administrator of the estate noted that they were neither married nor in a registered domestic partnership. However, my mother’s death certificate indicates that they actually were in a state registered domestic partnership. Does Probate Code 6402.5 come into play here? This section refers to possible heirs when the decedent has a predeceased spouse with children from another relationship, but the decedent has no issue or current spouse. This would apply to people in registered domestic partnerships too, yes?

If this section of code is applicable, do I send the death certificate to the court or does the court do an automatic check of the domestic registry?