I'm seeing a various Outlaws turning up in all the same places as a Harmon Holliman A.K.A Herman Holleyman and other spellings of the name.
The first family connection that I can identify is Harmon Holliman's Brother, Benjamin Holloman.
1753 Benjamin HollomanDiv of estate[Inv. 7 Feb 1752] Elizabeth Holloman, widow; John Holloman, William Holloman, and Mary Holloman orphans. Edward Outlaw was appt. gdn. to the orphans 8 May 1753, Bertie, NC
Upon reaching adulthood, John Holliman follows his uncle, Harmon Holliman, to what is now present day Franklin County, NC. John dies in 1770 naming his brother, William, and sister ,Mary, in his will. William turns up in Franklin Co., NC around the same time that his brother dies. He has land immediatly next door to his uncle Harmon. He and Harmon sell their land in Franklin and move to Wake County, NC on Sycamore Creek where the Raliegh airport is presently located. Harmon sold part of his Franklin land to William Outlaw of Bertie.
4 February 1770 Bute Co., NC (Later Franklin Co., NC) – Harmon Holoman of Johnston County, N.C. (Later Wake Co., NC) to William Outlaw of Bertie County, N. C. – the sum of 50 pounds Proclomation Money, for 118 acres lying and being in the Parish of St. John’s, beginning at Butts’ corner thence along his line to Anthony’s line &c. – to Ferrel’s Road to Prims’ corner &c. Witnessd: James Denby, Elias Stallions, William Hurd.signed Harmon H. Holomon.
After this, Harmon purchase land in Darlington Co. SC adjacent to George Outlaw.
Darlington County Deed Book B pg. 317 December 1804 Fadius Brown releases HARMON HOLLEYMAN of RICHMOND COUNTY, NC from a note due for 615 acres made up of adjoining tracts of 290 acres + 100 acres + 225 acres at the HEAD OF SPARROW SWAMP. (Transaction took place in 1804 but was recorded in 1809). George Outlaw, Mathew Skinner, Benjamin Skinner, Fadius Brown Jr., Issac Dubois, and Charles Price are adjacent land owners.