Many Hessians deserted to the American side during the Revolutionary War. The Continental Army actually actively tried to recruit Hessian deserters throughout the war. According to Professor of History at the University of Central Oklahoma, Charles Patrick Neimeyer, there were two major ways that the Continental Army tried to entice Hessians to desert; by offering property and by allowing captured Hessians to work in industries that helped the war effort, such as farming, forging tools and weapons, and making clothes. This was meant to show the Hessians that the republican way of life in America was superior. Hessian prisoners of war were often treated better than British prisoners of war as well as an attempt to entice them to join the Continental Army. The biggest desertion of Hessians came after the battle of Trenton, when Hessian prisoners of war were allowed to work on farms for pay. Many of these deserters ended up marrying American women and stayed in the United States even after the war was over. It is estimated that around 15,000 Germans did not return to Europe after the war, and only half of that number was due to death in the war. So, around 7,000 Hessians decided not to return to Europe after the war. I know that my answer may have been a bit more specific than you would have liked, dealing only with the Hessians, but I don't have any substantial knowledge on other groups of mercenaries employed by the British during the Revolutionary War. Anyway, hope this helps!