  We prove that a general complex Monge-Amp\`ere flow on a Hermitian manifold
can be run from an arbitrary initial condition with zero Lelong number at all
points. Using this property, we confirm a conjecture of Tosatti-Weinkove: the
Chern-Ricci flow performs a canonical surgical contraction. Finally, we study a
generalization of the Chern-Ricci flow on compact Hermitian manifolds, namely
the twisted Chern-Ricci flow.
