A bit about the Kotarski family history
The Kotarski family seems to derive from the southern part of Poland in the region around Krakow.
In common with many Polish names Kotarski has masculine (Kotarski) and feminine (Kotarska) forms of the name. Many families of Polish origin have abandoned this tradition. I find this rather sad but I can understand why having experience of the confusion that it causes.
Like millions of other people from central and eastern europe Kotarski's emigrated to the United States. The numbers are not large: 77 Kotarski and 29 Kotarska in the period 1893 to 1922. This probably reflects that Kotarski has always been quite a rare surname.
Just how rare? Kotarski is 9th out of 11 names which share 89.898% cumulative frequency in the 1990 US Census. So if I have my sums right the frequency of Kotarski is about 0.0001%. Which is about 1 in a million. Which is quite rare. Given that the population of the USA is nearly 295 million (at the time of writing) that would be roughly 300 Kotarski's in the USA. There are between 15 and 30 Kotarski's in the United Kingdom that are known about. This is roughly 1 in four million to 1 in two million.
I found this explanation of meaning of Kotarski:
Polish: habitational name for someone from a place called Kotarczyn in Płock voivodeship, Kotary in Częstochowa voivodeship, or Kotarz in Bielsko-Biała voivodeship.
This site also has a historical distribution of Kotarski families in the USA taken from the 1920 census.
So thats clear then.
Just so that we all know: a voivodeship is the biggest unit of local government in Poland.
The Kotarski family, or at least some part of it in the distant past, have a Coat of Arms. This has an interesting story which I shall relate on another occasion. For those who can't wait here it is. The Kotarski Coat of arms: