Balch - Family Distribution throughout the United States. I thought it would be interesting to take a look at the distribution of the Balch family throughout the United States. The map above shows where the greatest concentrations of Balches are in the country. California and Texas seem to come out on top with the most Balch family members. In the map the states with the lowest numbers of Balches are light blue while the states, with the highest concentrations of Balches, are red.