Final answer:
The part of the nail plate that goes beyond the finger's end is called the free edge, which is the furthest part from the nail growth center.
Step-by-step explanation:
The part of the nail plate that extends beyond the end of the finger is called the free edge. It is the portion of the nail that protrudes beyond the distal end of the digit and is what is typically trimmed or filed when managing nail length.
Regarding the question about which part is furthest from the nail growth center, the nail root is lodged deep in the epidermis and is the source of nail growth, while the eponychium is the nail fold that meets the proximal end of the nail body, also known as the cuticle.
According to the nail anatomy described, the part of the nail furthest from the nail growth center would be the free edge.