Lightly peel the potatoes and cut into bite sized pieces. Place in a pot of salted water and boil the potatoes for 5 to 10 minutes till fork tender, depending upon the size you cut them. While the potatoes are cooking in a bowl make the dressing by mixing the mayonnaise, pickle relish, sugar, white onion, mustard, vinegar, celery, pimento, carrot, parsley, pepper, and salt. When the potatoes are done and have cooled add the sauce and refrigerate for 2 hours. The best is if you allow this to sit overnight.