Hungarian term (edited): póthagyatéki eljárás

The Hungarian term "póthagyatéki eljárás" - in other words, "pótlólagos hagyatéki eljárás" - means the subsequent administration of the once closed estate due to newly discovered facts. In the probate court, first there is the original administration of the estate, which is the basic probate process (or proceedings). However, IF any further estate or will or heir is subsequently discovered, after the case (the estate) had been closed, it may be reopened and processed in probate court.

See the Hungarian definition of "póthagyatéki eljárás" from the current legislation:

Póthagyatéki eljárás

103. § (1) Ha a hagyatéki eljárás (jelen §-ban a továbbiakban: alaphagyatéki eljárás) befejezése után kerül elő a hagyatékhoz tartozó valamilyen vagyontárgy, póthagyatéki eljárásnak van helye. A póthagyatéki eljárásra a hagyatéki eljárás szabályait kell megfelelően alkalmazni.

(2) Az alaphagyatéki eljárásban tett nyilatkozatok és elvégzett eljárási cselekmények - az örökség visszautasításától vagy a visszautasítás jogáról való lemondástól eltekintve - a póthagyatéki eljárásra nem hatnak ki.

(3) A közjegyző a hagyatékátadó végzés meghozatalát megelőzően hivatalból intézkedik az alaphagyatéki iratok beszerzése érdekében.
http://net.jogtar.hu/jr/gen/hjegy_doc.cgi?docid=A1000038.TV

English definition and references:

Typically, a probate estate is reopened following the discovery of assets that were not discovered during the original estate administration. The Uniform Probate Code provides for this very scenario:

Section 3-1008. Subsequent Administration.

If other property of the estate is discovered after an estate has been settled and the personal representative discharged or after one year after a closing statement has been filed, the Court upon petition of any interested person and upon notice as it directs may appoint the same or a successor personal representative to administer the subsequently discovered estate. If a new appointment is made, unless the Court orders otherwise, the provisions of this Code apply as appropriate; but no claim previously barred may be asserted in the subsequent administration.
http://www.florida-probate-lawyer.com/probate/reopening-a-cl...

75-3-1008 Subsequent administration.
If other property of the estate is discovered after an estate has been settled and the personal representative discharged or after one year after a closing statement has been filed, the court upon petition of any interested person and upon notice as it directs may appoint the same or a successor personal representative to administer the subsequently-discovered estate. If a new appointment is made, unless the court orders otherwise, the provisions of this code apply as appropriate; but no claim previously barred may be asserted in the subsequent administration.
http://le.utah.gov/xcode/Title75/Chapter3/C75-3-S1008_180001...
http://www.legis.nd.gov/cencode/t30-1c21.pdf?20150226212626

Application / Petition for Subsequent Administration
In the Probate Court
http://www.sccourts.org/forms/pdf/334ES.pdf