Update: Effective January 1, 2013, the North Carolina legislature repealed the state's estate tax.
Previous to 2013, if a North Carolina resident died with a large estate, it might have owed both federal estate tax and a separate North Carolina estate tax. The state exemption amount was tied to the federal one, which means that for deaths in 2012, estates with a total value of up to $5.12 million were exempt from both state and federal estate taxes, but if an estate went over that amount, a North Carolina estate might owe both taxes.
Even estates of nonresidents might have owed North Carolina estate tax if the deceased person owned a lot of property in North Carolina—that is, real estate or other tangible assets located in the state.
However, now that North Carolina has eliminated its estate tax, most wealthy North Carolina residents will owe estate taxes only to the federal government. The federal estate tax exemption is $12.06 million in 2022, so only estates larger than that amount will owe federal estate taxes.
Before the repeal, property left to the surviving spouse was exempt from state estate tax, as it is currently exempt from federal estate tax--no matter what the amount. This is called the marital deduction. (There's one exception to the rule, for federal estate tax; noncitizen spouses cannot take advantage of the unlimited marital deduction.)
The executor will need to add up the date-of-death value of the deceased person's assets to determine whether or not federal estate tax returns are required. Pretty much everything the deceased person owned—real estate, cars, bank accounts, securities, retirement plan funds, and so on—is counted, whether or not it goes through probate or was held in a living trust. If the person made large taxable gifts (more than the annual federal gift tax exclusion amount, which is currently $16,000 per year per recipient in 2022), the taxable amount of those gifts is also counted as part of the estate.
If the deceased person owned assets with someone else, only the value of the deceased person's interest is included in the gross estate. For example, if the deceased person and his or her spouse owned a home together, half of its value will be included in the estate.
If the estate is large enough, the executor must file a federal estate tax return and pay any tax due nine months after the death. It's common to ask the IRS for an extension to file the federal return.
Federal returns are quite complicated. An executor who must file them will need to hire a lawyer or CPA who has lots of experience with these matters. The lawyer or CPA can be paid from the assets of the estate.