This is an interesting figure, taken from the 2008 USRDS (United States Renal Disease System) Atlas, which illustrates where patients in the U.S. are getting their dialysis from these days.
Nearly 63% of all patients are getting dialysis from one of the four LDO's ("large dialysis organizations"), the two largest of which by far are DaVita (94,000 patients) and Fresenius (84,000 patients) which for now are dominating the market. These numbers are actually from 2006 and do not reflect the fact that Fresenius has recently purchased the 3rd place company on the chart, "RCG" (Renal Care Group) and DaVita has recently purchased Gambro Dialysis centers.
Less than 7% of patients get their dialysis from SDO's ("small dialysis organizations"), a number which continues to decrease as a result of consolidation of dialysis power into the LDOs. The non-profit Dialysis Center, Inc. (DCI) accounts for about 13% of dialysis in the U.S. The remainder of patients are dialyzed by independent or hospital-based dialysis centers.