Once the date of death values have been determined for the decedent's assets, the next step in probating the estate is to pay the decedent's final bills and ongoing expenses of administering the estate.
It's the Personal Representative's job to figure out what bills the decedent owed at the time of death, determine if the bills are legitimate, and then pay the bills. The Personal Representative will also be responsible for paying the ongoing expenses of administering the estate, including legal fees, accounting fees, utilities, insurance premiums, and mortgage payments.
Once the Personal Representative/Executor has paid the decedent's final bills and has the estate expenses under control, the next step is to pay any income taxes and estate taxes that may be due.
Probate Checklist - 6 Steps to Probating an Estate