  We bound the nuclear dimension of crossed products associated to some partial
actions of finite groups or $\mathbb{Z}$ on finite dimensional locally compact
Hausdorff second countable spaces. Our results apply to globalizable partial
actions, finite group partial actions, minimal partial automorphisms, and
partial automorphisms acting on zero-dimensional spaces, or a class of one
dimensional spaces, containing $1$-dimensional CW complexes. This extends work
on global systems by Hirshberg and Wu.
