Have had a lot of success so far researching my Szacik and Kizior ancestors (Wiewiorka and Zassow), and I'm just starting to look for my Kozlowski and Kozik ancestors.
The Koziks will be hardest and most rewarding to research. Somewhere along the line and after coming to the states, The Kozik name was dropped in favor of Miller. My Great Aunt and My Great Aunt in law both have told me that the name was originally Kozik and that my 2nd Great Grandfather was the one that changed it in order to find work. The other thing I was told was that he was in the military in Poland and was "excused" from service after being involved in a duel with another man. Not being able to find work or possibly disgraced, he set off to America to start anew. No facts to back any of this up, just family stories passed down a few generations.
I have my Great Grandfathers Naturalization records and the approximate date in which he arrived in the States and I've also found the immigration record for Alexander Kozik (my G. Grandfather). He arrived in New York within a day or two of the date indicated on the naturalization record. He listed his destination as Webster, MA where he lived the rest of his live. His sponsor on the record is listed as his father.
I cannot find an entry in the 1900 census of Webster for any Kozik's or Millers. What I did find where a father and son, Albert and Alexander Mueller, boarders of a nice Polish family in Webster. Coincidence? Not sure. The search continues in Poland.