  We apply the local removable singularity theorem for minimal laminations and
the local picture theorem on the scale of topology to obtain two descriptive
results for certain possibly singular minimal laminations of $\mathbb{R}^3$.
These two global structure theorems will be applied in forthcoming papers to
obtain bounds on the index and the number of ends of complete, embedded minimal
surfaces of fixed genus and finite topology in $\mathbb{R}^3$, and to prove
that a complete, embedded minimal surface in $\mathbb{R}^3$ with finite genus
and a countable number of ends is proper.
