Sun completely!
If we suppose that the Moon will keep moving away 3.8 cm per year as it does today, it would have to pass 715 million years to experience no more a total eclipse of the Sun. It will be right, even when the Moon is to the closest distance to Earth, and the Earth to the furthest distance from the Sun (that is, the Moon being the largest ever possible, and the Sun the tiniest ever possible).
Although, in fact, the process is a little more complicated because as the Moon moves away from the Earth, the tides are slightly weaker, and, as a result, the Moon moves slower away, which would increase the time we have to keep observing total eclipses. However, in that timescale, the Sun would not be the same size, actually, it would grow a little bit, accelerating the effect that the Moon produces when moves away. As a consequence, the change of the Sun size would accelerate the process to leave us without total eclipses in about 500 million years more.
