  The seminal work of Eskin-Masur-Zorich described the principal boundary of
moduli spaces of abelian differentials that parameterizes flat surfaces with a
prescribed generic configuration of short parallel saddle connections. In this
paper we describe the principal boundary for each configuration in terms of
twisted differentials over Deligne-Mumford pointed stable curves. We also
describe similarly the principal boundary of moduli spaces of quadratic
differentials originally studied by Masur-Zorich. Our main technique is the
flat geometric degeneration and smoothing developed by
Bainbridge-Chen-Gendron-Grushevsky-M\"{o}ller.
