How is AC travel from a central to home?
There is no maximum distance AC current can travel, it is a wave. Waves need waveguides or transmission lines to propagate with little loss. The caveat is that for it to travel infinite distance, you'd also need your transmission media to be superconducting and lossless. 

In lossy lines the story is different, and is determined by the wavelength of the lines. After 1/4 wavelength the effects become significant.


  If a “long” line is considered to be one at least 1/4 wavelength in
  length, you can see why all connecting lines in the circuits discussed
  thusfar have been assumed “short.” For a 60 Hz AC power system, power
  lines would have to exceed 775 miles in length before the effects of
  propagation time became significant. Cables connecting an audio
  amplifier to speakers would have to be over 4.65 miles in length
  before line reflections would significantly impact a 10 kHz audio
  signal!  


Source: https://www.allaboutcircuits.com/textbook/alternating-current/chpt-14/long-and-short-transmission-lines/