"Boros-" or "Boris-" is the root or stem of several surnames, all based on the convention of naming a child using an ancestor's given name. This is very common among Scandinavians as seen in such names as Alfred Jensen or Jenson, i., Alfred, descendant of someone named Jens (John) or Carl Larson, i.e., Carl, descendant of someone named Lars. The Lithuanian version of this convention is seen is the name, Kazimieras Borisevic^ius, i., Casimir (or commonly Charles in the U.S.), descendant of someone named Boris. Borisevic^ius is actually a Lithuanian version of the Polish Borisewicz.
Here are extracts from other posted messages online, mostly from Fred Hoffman, published author about this naming process:
Russian vs Lithuanian names
BORISEVIC^IUS is the Lithuanian equivalent of Polish BORYSEWICZ or BORYSEWICZ or BORYSIEWICZ. It means "son of Boris." There's some info on that first name here:
Note that a Russian who is the son of a man named Boris would have Borisevich as his middle name. Thus if a Russian named Ivan Karpov was the son of a man named Boris, Ivan's full, formal name in Russian would be Ivan Borisevich Karpov. Russians use these so-called patronymics -- names meaning "son of" -- as middle names, but not very often as surnames. In Belarusian and Polish (and many other Slavic languages as well) they came to be used primarily as surnames.
So a Lithuanian who went by BORISEVIC^IUS might show up on documents with his name in the Russian form BORISEVICH or the Polish form BORISEWICZ. There's nothing unusual about this at all.
Boris is a first name used primarily by Eastern Slavs, that is, Belarusians, Russians, and Ukrainians, and by Southern Slavs, for instance, Bulgarians. It's not a name that ever caught on among the Poles or Lithuanians. A family named BORISEVIC^IUS probably had an ancestor who came from farther east, from Belarus or Russia. In those areas, the first name Boris is pretty common, so trying to tell anything from your family by analyzing BORISEVIC^IUS is a little like trying to tell something about an American family from a surname such as DAVIDSON. It doesn't tell you much, except the first name of an ancestor several centuries ago -- one who probably came originally from Belarus or Russia or Ukraine.
AUDYCKI (pronounced roughly "ow-DITT-skee") is a Polish version of the Lithuanian surname AUDICKAS (roughly "ow-DITTS-koss"). According to the Lithuanian Surname Dictionary, that surname probably developed from the Belarusian first name Avdiy or Avdei or Ovdei, so that it meant "of the kin of Avdiy" or "one from the place of Avdiy." That first name is an East Slavic version of the Biblical name we know as Obadiah http://www.behindthename.com/name/obadiah).
You might wonder why these names would appear in Polish forms. During the period when most folks emigrated from Lithuania, it was ruled by the Russian Empire, which had made it illegal to use any language but Russian in official documents. That meant when a Lithuanian emigrated, his papers were all in Russian, and his name appeared in Russian form, spelled in the Cyrillic alphabet. Obviously, as he headed west, at some point it would be necessary to render that Cyrillic form in our alphabet.
Remember that back then, Lithuanian had never really come into much use as a written language. That was beginning to change as of the late 19th century, but there was still no consensus on how Lithuanian was to be spelled. So there weren't that many officials familiar with the Lithuanian forms of surnames. Very often, the person who rendered the Cyrillic spelling in our alphabet spoke Polish; he would tend to write the name in the form that seemed correct to him. To a Pole, AUDICKAS was an obscure form of the name; AUDYCKI would seem much more reasonable.
So even if a person was called BORISEVIC^IUS or AUDICKAS back home, his papers were likely to refer to him as BORISEWICZ or AUDYCKI. There were plenty of exceptions, of course. But the Polish versions of these names were the most familiar ones available in the Roman alphabet. Also, before Russian was mandated as the official language for all documents, Polish had served that role in Lithuania. So there was a tradition of writing names down in their Polish form. It wasn't until Lithuania gained its independence after World War I that you start seeing documents with Lithuanian forms of names. Before then, they were usually either Russified or Polonized.