from the 13th c. on entire regions were left empty when people fled or died from plagues or wars or from a bloody invasion (like the Mongol invasion of Europe or the Ottoman invasion). after these disasters the re-settling process started automatically thanks to the free migration within the Kingdom of Hungary and later in the Habsburg Empire , but in the end it was the rulers privilege to bring in new settlers.

in the 16th c. the disaster of Mohacs left the southern part of KoH empty, what made southern slavic people possible to freely migrate to south-east Hungary and settle in the region. in the 18th c. after the Ottoman occupation and a failed Independence war, vast regions of the former Kingdom of Hungary (then part of the Habsburg Empire) were left empty. these regions were resettled mainly by western swabians and other nationalities in the early 18th c.

in hungarian Horvát originally meant "someone who speaks southern slavic", or comes from a southern slavic land or wears southern slavic clothes. the 17th c. light hussar cavalry was also called horvát, so it has a military meaning aswell. some settlers magyarized their slavic name to Horvát or Horváth, or it could simply stuck on someone for being southern slavic.

when the name is written like Horvát or Horváth (Croatia, Hungary, Slovakia, Austria) you can almost be sure that the owner had a southern slavic ancestor in the Kingdom of Hungary.

so, Horvat is a widespread family name, thanks to migration and re-settling in KoH and Habsburg Empire (but before it became A-H).