Hedgehog,
Before tackling District Archives/RAHS (records kept under 75 yrs old mostly),
start w/LDS.
If indeed there are no records for Kosovets at Regional level (75-100 yrs old),
as has been suggested, you will have to obtain a PRIVACY RELEASE thru either
Ukrainian Embassy or Consulate in nearest you, in order to get copies of specific
records from RAHS. At RAHS level, they do no research.
Current cost to obtain Privacy Release documentation is appx $100 USD.
LDS has all FYI info available on site.
An exc resource for Halyczyna/Galicia Research:
Genealogy of Halychyna and Eastern Galicia
Genealogy of Halychyna and Eastern Galicia
Notice that I didn't even start to explain the 30 yr period in Vienna and
final settlement in Jaroslaw. Family legend is frequently just that. Let's
wait and see where records will lead you.
____________________________________________________
Irene has only been a poster here for a short time, so make sure
to get proper references. I cannot recommend her, because I do not
know her. I do know she used a source I provided her to create
an opportunity for herself w/you.
Bare in mind that given the Ukrainian economy it is very easy to acquire
relatives in Ukraine, that may not be your own. Be careful.
In order to view just how frequently your surname shows up on
Google.com, add Ukrainian under Language Tools. Submit your
surname using Cyrillic.