Gov. Chase Osborn, in his autobiographical The Iron Hunter (1919), suggested that all of the Osborns in the US were descended from 2 or 3 brothers. From limited work on my line and several others, it is hard for me to see how this could be the case.

There are a number of genealogical "islands" of Osborns (my focus has been on that spelling, but over generations the adding or omitting of a terminal "e" has been noted, as well as other alternate spellings within the same family lines). That is, the lines as far as can be traced back, (1) do not join, and (2) appear to begin over a geographical range that suggests multiple entries into the eastern colonies from Nova Scotia to the Carolinas (at least).

Probably someone has considered this subject more extensively and insightfully than I (an interloper in genealogy), but for what it's worth, here is some of what I've observed in the WikiTree data (the "island" names are purely subjective, based on some notable characteristics of the line in question; addition of numbering is based on the random ordering, and has no significance other than as another aid in referencing):

1. Governor's island: C.S. Osborn's line, going back to Jacob Osborn of New Jersey.
2. Ozias' island: My lineage, going back to three successive Ozias's, the first and second of whom died relatively young, in Massachusetts and upstate New York.
3. Railroad & eugenics island: Goes back to railroad tycoon William Henry Osborn, originally of Salem, Massachusetts, of whom a son, Henry, and a grandson, Frederick, were notables involved in, among other things, the eugenics movement.
4. Pittsfield & entomology island: Richard Osborn and descendants, including noted entomologist Prof. Herbert J. Osborn, who moved from western Massachusetts to the Midwest.
5. Fairfield & Oneida island: Descendants of Richard Osborn for several generations mostly in sw Connecticut and east central New York.
6. Tristate island: Apparently goes deep in Kent County, England (John Osborne), with a Thomas Osborne and descendants for several generations in New Haven area of Connecticut, Long Island, New York, and northern New Jersey. This appears to be the largest "island" among those identified here. One branch includes former Civil War brig. general (Union) and US Senator (from Florida) Thomas W. Osborn.
   1. Reuben's isthmus: Rev. Reuben Osborn appears in the record with no information on parents. However he married into another Osborn line through his wife, Hannah Osborn.
7. Enfield & Hartford County island: Several generations in north central Connecticut and perhaps across the border into Massachusetts, descended from James Osborne.
8. Massachusetts & Ohio island: Descendents of Alexander Osborn of Hampden County, Massachusetts, who relocated to Geauga and Ashtabula counties in Ohio.
9. Puritan & Quaker island: Descendants of John Osborn, who arrived in Massachusetts during the Puritan Migration, among whom were Quakers who lived in the adjoining counties of Litchfield, Connecticut and Dutchess, New York.
10. Massachusetts & Nova Scotia island: Descendants of Rev. Samuel Osborne, who came to Boston from Ireland, and whose descendants (at least some of them) moved to Nova Scotia.
11. Delaware & North Carolina island: Descendants of Robert and son Matthew, Sr. (spellings of surname vary), who came to Delaware & North Carolina from England; later generations of whom were in various states to the west.
12. Virginia, Kentucky & Arizona island: Descendants of James Osborne, notably Jonathan Osborne who came to Virginia from England in the early 1700s. Mainly in Virginia and Kentucky, with some in NC and Tennessee, and one branch in Arizona, including a governor of that state, Sidney Preston Osborn.
13. Kentucky & Indiana island: Descendants of Matthew Osborne or Osburn.
14. Maryland, Carolinas & Ontario island: Descendants of William Osborn Jr., who came to Baltimore in the late 1600s. Many in North Carolina. One, James Ozburn, was a Loyalist during the American Revolution, and migrated to Upper Canada (Ontario).
15. Pennsylvania & Ohio island: Descendants of John Osborn, who moved west from Pennsylvania to Ohio and later other states (Indiana, Illinois, Missouri, Texas).
16. Virginia & Kentucky island: Descendants of John Osbourne, of Virginia and then Kentucky (y-line appears to end there, per data available on WikiTree as of writing).

And certainly others. Am working to add some from the Southern Colonies of what became the US.

Some of these "islands" may be easily joined - or perhaps already have been by others elsewhere (do you have info?). Of course as one goes back in time, it is harder to be sure of the data and actual relationships.

Nevertheless, the purpose of listing these islands in this manner is to facilitate attention to each, including verifying information on when specific individuals surnamed Osborn (and spelling variants) arrived to settle in North America, and then how they are related further back in time.