Final answer:
Flat end wraps provide the most control over hair ends by covering and smoothing them before rolling onto a perm rod, which prevents fishhooks and ensures a uniform curl pattern.
Step-by-step explanation:
The type of end wrapping that will provide the most control over the hair ends is flat end wraps. This technique involves using end papers in such a way that the ends of the hair are completely covered and smoothed before rolling them onto a perm rod or curler. By doing this, you can prevent fishhooks and ensure even distribution of the hair across the perm rod, which is crucial for achieving a uniform curl pattern.
Another common method is the bookend wrap, where one end paper is folded in half over the hair ends, but it might not provide as much control as a flat wrap. It's important to select the type of end wrapping that best suits the length and texture of the hair, as well as the desired outcome of the style you are looking to achieve.