Relative blocking sets of unions of Baer subplanes

We show that, for small t, the smallest set that blocks the long secants of the union of t pairwise disjoint Baer subplanes in PG (2 , q2) has size t(q+ 1) and consists of t Baer sublines, and, for large t, the smallest such set has size q2+ q+ 1 and is itself a Baer subplane of PG (2 , q2). We also present a stability result in the first case