Who is responsible for determining estate value at death and if any tax is due?

Some people have an Executor (male) or Executrix (female) in their Will to take care of these duties. Other people have "Trust companies" that will do it as well for a fee. Both parties have to probate the Will to be sure all debts including property and personal taxes off and the residue that is left after that is the total amount of the Estate. Marcy