  In this paper, we prove that any mean curvature flow translator $\Sigma^2
\subset \mathbb{R}^3$ with finite total curvature and one end must be a plane.
We also prove that if the translator $\Sigma$ has multiple ends, they are
asymptotic to a plane $\Pi$ containing the direction of translation and can be
written as graphs over $\Pi$. Finally, we determine that the ends of $\Sigma$
are strongly asymptotic to $\Pi$ and obtain quantitative estimates for their
asymptotic behavior.
