Not sure about the actual etymology of planina but indeed it is related with Ukrainian polonyna.
In Polish we say polonina under ukrainian influence, although a polish version should sound plonina if we followed the language system.
All of the above mentioned words originated from protoslavic polnina. There are different eastern, southern and western slavic variations, because of the so called TerT, TelT/TorT,TolT groups.
(For instance protoslavic bolto for "mud" is realised as bloto in Polish, boloto in Ukrainian and blato in Slovenian).
Here it gets a bit tricky, because we can't be sure where to derive the above mentioned protoslavic polnina from. For sure it's a noun built by adding the -ina suffix to an adjective polny. It's not clear for me what this adjective meant at the time.
It can come both from:
- pole "field"
- polny (plany/plony/polonyj) meaning "unproductive, infertile, arid"
- something else maybe (?)
Anyway both of those above mentioned have a meaning related to a ground that doesn't give yield - desertous or at least lacking forest, which probably wasn't very common on slavic territories in the middle ages.
(Sorry for no Polish characters in the post).
But which Boruta d'ya mean? 
) ? 
