  Asymptotic quadratic growth rates of saddle connections and families of
periodic cylinders on translation tori with n marked points are studied. For
any marking the existence of limits of the quadratic growth rate is shown using
elementary methods (not Ratners theorem). We study the growth rate limit as
function of the marking. We give precise formulas for this function in the case
of two marked points and describe the sets where the growth function is maximal
and continuous in any case. For rational two markings we calculate the index of
the Veech group in SL(2,Z) using two different ways.
