Need a simple, non-legalese “executor" definition? An executor is the person who handles a deceased person's estate, making sure all property is distributed according to the decedent's wishes and that all debts are paid. Usually, executors are close family members of the deceased—spouses, children, parents, or siblings—but the person writing a will (the “testator") can choose anyone to fulfill this role.
On the other hand, if you are not responsible for its tax, then you should declare the equipment in Part III of the Business Property Statement (Equipment belonging to others). Where equipment is declared in Part III of the Business Property Statement, the Assessor will also send a Notice to File to the person reported as the equipment's actual owner.