Final answer:
The length of time between avulsion and replantation is the most crucial factor for the success of a totally avulsed tooth's replantation, with immediate action being paramount.
Step-by-step explanation:
The most important factor concerning the success of replantation of a totally avulsed tooth is the length of time between avulsion and replantation. Immediate replantation, ideally within the first hour, can significantly improve the prognosis for the tooth survival. It is critical to keep the avulsed tooth moist, and if professional dental care is not immediately available, placing the tooth in a suitable medium such as saliva, milk, or saline solution can be temporarily helpful. However, it should be noted that the primary determinant of success is how quickly the tooth is replanted into the socket.