  We consider a system of three surfaces, graphs over a bounded domain in
${\mathbb R}^2$, intersecting along a time-dependent curve and moving by mean
curvature while preserving the pairwise angles at the curve of intersection
(equal to $2\pi/3$.) For the corresponding two-dimensional parabolic free
boundary problem we prove short-time existence of classical solutions (in
parabolic H\"{o}lder spaces), for sufficiently regular initial data satisfying
a compatibility condition.
