Fees for an executor, and the attorney for the executor, are outlined in Probate Code Sec. 10800 and 108100.
Basically, the executor of a probate estate is entitled to a percentage of the estate for their services to the estate. The percentage is a sliding scale based on the value of the estate. Also, keep in mind that the value of the estate for determining the fees is based in the gross value of the estate, not the net (assets - debt).
These fees, however, must be accounted for in the probate filings and approved by the court.
If you are concerned that your father may not be able to handle this responsibility by himself, he should seek the assistance of any attorney in settling your Aunt's estate.
Disclaimer: This answer does not constitute legal advice, nor does it create an attorney-client relationship. You should contact an attorney to discuss the specifics of your matter.
The fees for an executor are set forth by statute in the Probate Code. The fee will depend upon the gross value of the estate that is probated: 4% of the first $100,000, 3% of the net $100,000, 2% of the next $800,000, 1% of the next $9 million, etc. For a $1 million estate, the executor's fee is $23,000.
There is also the ability to obtain "extraordinary compensation" for extraordinary services, such as filing the estate tax return (if one is necessary) or handling any estate litigation. These fees may be awarded by the court, and their dollar-value is not dictated by statute.
Disclaimer: This general response is not intended to create an attorney-client relationship.
The above answers are assuming that the estate is going through the court-supervised probate process. If it isn't, and if there is no restriction on compensation in the will, then your father is entitled to 'reasonable compensation.' If it is going through the court-supervised probate process, then your father can petition for partial compensation as early as 4 months after the issuance of letters. He should sit down with a probate attorney to discuss the matter.