Once a person dies, either the persons Will has to be probated or an Heirship must be done should the person die without a Will. An estate administration is the result of the probate of the Will or Heirship determination. Heirship determinations are a statutory based determination of who will receive the estate based mainly on the persons descendants.
An independent means that their is no court supervision of the administration of the estate. A dependent administration is where the court supervises the estate and the administrator must secure permission for acts done to settle and take care of the estate.