As noted, the territory of most counties includes that of municipalities, within and smaller than the respective counties. However, there are three kinds of exceptions to this arrangement:
1.By a series of annexations or other mergers, a city government may come to have exactly the same territory as the county that contains it, even though they remain separate governments. This is nearly the case in Jacksonville, Florida, which has incorporated all of Duval County except for four smaller suburban cities.
2. Several cities and counties around the country have consolidated city-county governments and are considered both a city and a county under state law. Denver, Colorado and San Francisco, California have been coextensive with their respective counties since the counties were created. On the other hand, Indianapolis, Indiana; Louisville, Kentucky; Philadelphia, Pennsylvania; and Nashville, Tennessee unified with their respective counties after the two entities existed separately. There is also the "City and County of Honolulu", but this is unlike the others in that Hawaii has no incorporated cities and thus the "city" part of "city and county" is in this case a misnomer. Honolulu County contains the entire island of Oahu, which includes many dozens of communities and rural areas in addition to the urban area designated as the Honolulu CDP. Prior to its abolition, the government of Suffolk County, Massachusetts was largely administered by the Boston city council. In Nantucket County, Massachusetts, the Town of Nantucket board of selectmen act as county commissioners. 
3. The area now forming the five boroughs of New York City consisted, into the late 19th century, of three typical counties and parts of two others, each containing at least one city or town. These are still counties in name and in state law; nevertheless, since 1898 they have been entirely contained within the boundaries of the city, and following the creation of Bronx County in 1914, each borough now corresponds exactly to one county.
4.In several states (including Alabama, Colorado, Georgia, Michigan, Minnesota, Mississippi, North Carolina, Ohio, Tennessee, Texas, Utah, Washington and Wisconsin), a city may annex land within an adjacent county. That land is then subject to city government, but the respective counties continue to provide county-specific services and residents vote for county officials in the respective counties. Major cities that lie in multiple counties include:Atlanta, Georgia; Birmingham, Alabama; Chicago, Illinois; Houston, Texas; Kansas City, Missouri; Oklahoma City, Oklahoma, and Amarillo, Texas. The city of Appleton, Wisconsin lies within three counties (Outagamie, Calumet, and Winnebago), and is the county seat of Outagamie County. The city of Aurora, Illinois, a populous outlying suburb of Chicago, lies within four
counties (Kane; DuPage; Will; and Kendall).
5. In Michigan, the city may petition to change the county boundaries to accord with the city boundaries. Historically, however, this has rarely been exercised. There are many cities that span county boundaries in Michigan.
StatisticsMain article: County statistics of the United States
At the 2000 U.S. Census, the median land area of the 3,066 U.S. counties was 1,611 km² (622 sq. miles), which is only two-thirds of the median land area of a ceremonial county of England, and only a little more than a quarter of the median land area of a French département
This figure, however, hides large differences between the eastern and western United States. The land area of counties in the western United States is much larger than the land area of counties in the eastern United States. For example, in the eastern United States the median land area of counties in Ohio is 1,138 km² (439.5 sq. miles) and in Georgia it is 888 km² (343 sq. miles), whereas in the western United States the median land area of counties in California is 3,977 km² (1535.5 sq. miles) and in Utah it is 6,286 km² (2,427 sq. miles)
By area, the largest county in the United States is North Slope Borough, Alaska at 94,763 square miles (245,435 km²) and the smallest county in the United States is Kalawao County, Hawaii at 13 square miles (34 km²). (The largest county in the 48 contiguous states is San Bernardino County, California, at 20,105 mi²/52,073 km², and the smallest is Arlington County, Virginia at 26 mi²/67.6 km².)
However, when county equivalents are included, both lose their status. The largest county equivalent by area is Yukon-Koyukuk Census Area, Alaska at 147,843 square miles (382,912 km²) and the smallest is the independent city of Falls Church, Virginia at 2.0 square miles (5 km²).
At the 2000 U.S. Census, the median population of the 3,066 U.S. counties was 24,544 inhabitants, which is 33 times less inhabitants than the median population of a ceremonial county of England, and 21 times less inhabitants than the median population of a French département
At the 2000 U.S. Census, only 16.1% of U.S. counties had more than 100,000 inhabitants, while 83.9% of U.S. counties had less than 100,000 inhabitants. This reflects the essentially rural nature of U.S. counties, whose grid was designed in the 19th century, in a country still largely rural and only marginally affected by urbanization. Today, the vast majority of people in the United States are concentrated in a relatively small number of counties.
The most populous county (or county equivalent) is Los Angeles County, California with 10,226,506 people as of 2005, and the least populous county is Loving County, Texas with 67 people as of 2000.
The most densely populated county (or county equivalent) is New York County, New York with 66,940 people per square mile (ppsm) as of 2000, and the least densely populated county is Lake and Peninsula Borough, Alaska with 0.08 ppsm as of 2000. The least densely populated county equivalent is Yukon-Koyukuk Census Area, Alaska with 0.04 ppsm as of 2000.