Toe nail re-growth question. What speed does a toenail come back out?

1 year. It takes approximately one year for a toenail to grown from the base to the tip of the toe.
About 6 mo to 1 yr. Toenails do not grow as fast as those of the fingers and depending on how fast your body produces keratin, the substance which nails (and hair) are made of, regrowth can take between 6 months to 1 year; in some cases longer. Other factors that can alter the rate of regrowth include age, previous injury to the nail matrix or nail plate and any other condition that can affect nail growth properties.
Toe nail growth. Toe nails grow at an average rate of 0.1 mm/day (1 cm every 100 days). Fingernails require 4 to 6 months to regrow completely. Toenails require 12 to 18 months. Actual growth rate is dependent upon age, season, exercise level, and hereditary factors.