  In this paper, we prove that any mean curvature flow translator $\Sigma^2
\subset \mathbb{R}^3$ with finite total curvature, quadratic area growth, and
one end must be a plane. We also prove that if the translator $\Sigma$ has
multiple ends, they are asymptotic to a plane $P$ containing the direction of
translation and can be written as graphs over $P$.
