  We propose a model of semi-vicious walkers, which interpolates between the
totally asymmetric simple exclusion process and the vicious walkers model,
having the two as limiting cases. For this model we calculate the asymptotics
of the survival probability for $m$ particles and obtain a scaling function,
which describes the transition from one limiting case to another. Then, we use
a fluctuation-dissipation relation allowing us to reinterpret the result as the
particle current generating function in the totally asymmetric simple exclusion
process. Thus we obtain the particle current distribution asymptotically in the
large time limit as the number of particles is fixed. The results apply to the
large deviation scale as well as to the diffusive scale. In the latter we
obtain a new universal distribution, which has a skew non-Gaussian form. For
$m$ particles its asymptotic behavior is shown to be
$e^{-\frac{y^{2}}{2m^{2}}}$ as $y\to -\infty $ and
$e^{-\frac{y^{2}}{2m}}y^{-\frac{m(m-1)}{2}}$ as $y\to \infty $.
