The process of undergoing probate in a secondary location is known as ancillary probate.
Personal property (such as a bank account or coin collection) is generally probated in the decedent's legal state of residence, but real estate is probated where the property is physically located. Certain classes of personal property, such as vehicles that are registered and titled out of state, may also need to be probated in the jurisdiction where the property is domiciled.
If there are multiple real properties in a single state, you can probate them all in the same probate court, but if the decedent owned property in multiple states or internationally, you'll have to go through the settlement process in multiple locations.
The first thing to check is to see whether the out-of-state property was held in some version of joint tenancy or tenants in common (different jurisdictions have different legal variations on this). If so, the remaining owners will automatically retain ownership of the property, and while they will probably want to clean up some records to remove the deceased, there will be no need for any ancillary probate.
Some jurisdictions support Transfer-on-Death Deeds, which automatically transfer ownership to named beneficiaries upon the death of the owner. In such cases, the executor will have to show proof of death, but no ancillary probate or even small estate settlement process will be needed.
Similarly, if the property was held in trust or a retirement fund or basically anything with a named beneficiary, there will usually be no need for any ancillary probate proceedings, and the normal beneficiary transfers can occur as defined by law.
Even if the transfer is "automatic", transferring real estate is more complex than transferring ownership of other asset classes, and an amended deed to the property must usually be filed with the local courthouse or tax assessor's office.
If there is no automatic transfer of the property, then you should check to see if the secondary jurisdiction supports simplified approaches for estate settlement of small or simple estates. If you are only probating a single property in a given jurisdiction (i.e., state), it's likely that this portion of the estate will qualify for a simplified approach ... which sometimes may involve no or very limited court involvement.
See small estates for state-specific details, and if an estate includes Canadian real estate, you can check the Canadian version of EstateExec for Canadian province-specific rules for small estates.
If none of the above conditions apply, then you will have to apply for probate in the appropriate out-of-state court.
Probating a portion of an estate in a secondary location is generally known as ancillary probate, and fortunately many out-of-state courts have simpler processes for such probate, given that a primary probate exists elsewhere and is being managed through a legal court process.
If there was no need for probate in the decedent's home jurisdiction, but the decedent owned property elsewhere, then the process of probate in the out-of-state jurisdiction will be known as non-domiciliary probate, not ancillary probate.
If there is a will, the fact that certain property must be probated in a different jurisdiction should not affect overall residuary estate distribution percentages to heirs, although it may impact who gets what (for example, in jurisdictions such as PR and GU, an executor must follow strict rules about who may inherit land)
To make this more concrete, suppose John died leaving his $1M estate to be divided equally among his wife and 3 children (so each heir would receive 25%). If for some reason a $200K out-of-state property went solely to one of his children, then that amount would be included in the overall distribution calculations, so that the other heirs would each receive $250K from the primary estate, and the child who inherited the out-of-state property would receive only $50K from the primary estate.
If there is no will, the distribution of the estate must follow the intestate succession laws of the relevant jurisdictions, meaning that the primary estate must be distributed according to the laws of the decedent's home state, but any real estate existing outside that home state must be distributed according to the local intestate succession laws. Thus, the heir percentages could be different, and different heirs could be involved entirely.
There may be subtle legal issues here, so if your situation is complicated or the heirs are not cooperative, you may want to seek the advice of a lawyer, or even a lawyer in both jurisdictions.