Small maximal partial spreads in classical finite polar spaces

We prove lower bounds on the size of small maximal partial spreads in Q(+)(4n + 1, q), W(2n + 1; q), and H(2n + 1; q(2)). This research on the size of smallest maximal partial spreads in classical finite polar spaces is part of a detailed study on small and large maximal partial ovoids and spreads in classical finite polar spaces, performed in [5, 6].