Topological Type of Limit Laminations of Embedded Minimal Disks

We consider two natural classes of minimal laminations in three-manifolds. Both classes may be thought of as limits - in different senses - of embedded minimal disks. In both cases, we prove that, under a natural geometric assumption on the three-manifold, the leaves of these laminations are topologically either disks, annuli or Moebius bands. This answers a question posed by Hoffman and White.