PE funds are usually limited partnerships (LPs), which gives them special privileges of nondisclosure; most are organized in the State of Delaware. PEF's have sponsors, or "principals," who are responsible for organizing the fund and recruiting other investors. They are never "limited liability partnerships" (LLP's); apologies to Urban Dictionary for erroneously mixing them up in my definition for "private equity fund" and "hedge fund." The difference between the two is explained there.
Among the best-known PE funds are Blackstone Group*, Kohlberg Kravis Roberts (KKR)*, Goldman Sachs Capital Partners*, Carlyle Group, Permira, Apollo Management, Providence Equity, TPG Capital, Warburg Pincus, and Cerberus. Companies marked with an asterisk (*) are publicly listed corporations; most PE funds are privately managed. The selection above includes the largest ones by capital under management.
In the USA, PE funds have long been sinecures for the most powerful political dynasties: the Rockefellers, the Romneys, the Bushes, and others.