This is the 15662nd most frequent Russian word.
принадлежавших
"Belonging to" (plural, past tense).
In this sentence, "принадлежавшие" is used as a participle and describes the state to which the buildings belonged.
Здания, принадлежавшие государству, были отремонтированы.
The buildings that belonged to the state were renovated.
Here, "принадлежавшие" is used to indicate possession of the documents by her ancestors in the past.
Она нашла документы, принадлежавшие её предкам.
She found documents that belonged to her ancestors.
In this example, "принадлежавшие" specifies that the paintings were formerly the possession of the famous artist.