  Let X be a smooth projective connected curve of genus $g \ge 2$ and let I be
a finite set of points of X. Fix a parabolic structure on I for rank r vector
bundles on X. Let $M^{par}$ denote the moduli space of parabolic semistable
bundles and let $L^{par}$ denote the parabolic determinant bundle. In this
paper we show that the n-th tensor power line bundle ${L^{par}}^n$ on the
moduli space $M^{par}$ is globally generated, as soon as the integer n is such
that $n \ge [\frac{r^2}{4}]$. In order to get this bound, we construct a
parabolic analogue of the Quot scheme and extend the result of Popa and Roth on
the estimate of its dimension.
