  For given integers $r$ and $\ell$ such that $2\leqslant\ell\leqslant r-1$, an
$r$-uniform hypergraph $H$ is called a partial Steiner $(n,r,\ell)$-system, if
every subset of size $\ell$ lies in at most one edge of $H$. In particular,
partial Steiner $(n,r,2)$-systems are also called linear hypergraphs. The
partial Steiner $(n,r,\ell)$-system process starts with an empty hypergraph on
vertex set $[n]$ at time $0$, the $ \binom{n}{r}$ edges arrive one by one
according to a uniformly chosen permutation, and each edge is added if and only
if it does not overlap any of the previously-added edges in $\ell$ or more
vertices. In this paper, we show with high probability, independent of $\ell$,
the sharp threshold of connectivity in the algorithm is $ \frac{n}{r}\log n$
and the very edge which links the last isolated vertex with another vertex
makes the partial Steiner $(n,r,\ell)$-system connected.
