The amount of pronation/supination of your hands affects which muscle groups will be affected the most. Most people look at the arm and see three muscle groups: triceps, biceps, and forearms, but there are actually more like 5 due to the brachialis and brachioradialus.
The brachialis is buried under your bicep, and when larger will help push it up. The brachioradialus is that baseball shaped muscle on top of your elbow joint. Put your hand on top of your bicep and make a curling motion with your hand at different angles and you'll feel what I'm talking about.
Depending on your routine in may be necessary to have one or more isolation exercises for the arm to promote maximum growth. For example, if you do supinated chinups you may not need standard curls, but reverse curls would probably be a good thing. Hitting your arms with different exercises and different angles is the best way to ensure maximum growth. Don't think just using regular dumbbell and barbell curls is enough variety.