Many soldiers just went home. However, they usually turned themselves in to a nearby Federal unit to receive some sort of official release as their government and army no longer existed. Without a parole or evidence they had taken the oath of allegiance, they would have a hard time dealing with the forces that occupied their home areas. The majority of Lee's cavalry cut their way through Union lines at Appomattox, and escaped the actual surrender. These units disbanded at various places and eventually the individuals obtained paroles and took the oath of allegiance.For example...My G-G-Uncle was a POW at Camp Chase, Ohio and Point Lookout, Maryland from August 7, 1864 until March 18, 1865. On March 18 he was paroled and exchanged. Given 30 days to report back to his unit, the 22nd Virginia Cavalry, he was at home when Lee surrendered. After the surrender was known, he reported to a nearby Federal unit with his parole papers and took the oath of allegiance, thereby freeing himself up to get on with his life. A cousin of his, who was still with the 22nd Va. Cav. when Lee surrendered, was one of the few left when the unit disbanded at Lynchburg, Virginia a few days after the surrender. He was paroled at Lynchburg on April 15, 1865. These two ancestors of mine served in the 22nd Virginia Cavalry with one Sgt. John Wilson Vermillion, better known to Western fans as "Texas Jack" Vermillion. You can take the notation "deserted" with a grain of salt, as it were. The record keeping of both armies left a lot to be desired although the Confederates were more lax than the Federals. Sometimes a man was listed as dserted or AWOL just because he was not present at a muster. Not being present at muster did not mean he was not around somewhre on duty. I had an ancestor who was listed as deserted when he was sick in hospital.