  Multiples zeta values and alternating multiple zeta values in positive
characteristic were introduced by Thakur and Harada as analogues of classical
multiple zeta values of Euler and Euler sums. In this paper we determine all
linear relations among alternating multiple zeta values and settle the main
goals of these theories. As a consequence we completely establish
Zagier-Hoffman's conjectures in positive characteristic formulated by Todd and
Thakur which predict the dimension and an explicit basis of the span of
multiple zeta values of Thakur of fixed weight.
