Here is an update to the Y-DNA study. Four Papez men have been tested so far, and 3 of those 4 have been found to be relatively closely related, matching on all 26 markers. These 3 belong to the I1a Haplogroup (for Haplogroup descriptions, see
https://www3.nationalgeographic.com/genographic/atlas.html) and all have ancestors in towns near Zuzemberk, Slovenia.
The fourth participant, whose ancestors hail from Trzisce (north of Novo Mesto) appears to belong to Haplogroup G2. This suggests that at least two separate Slovenian groups of people adopted the surname Papez. This came as something of a surprise since the ancestral villages are separated by less than 20 miles. This fact, combined with the small overall population of Slovenia and relatively clustered distribution of the surname, caused one to suspect a common origin for all (Slovenian) Papezes. These contradictory results will subsequently help us direct our paper records search to expect or rule out relationships between families.
We are presently awaiting tests on a distant cousin to confirm a suspected paper relationship, as well as a family from Crnomelj in Bela Krajina near the Croatian border with no known paper connection.