  We make some remarks about bubbling on, not necessarily proper, champs de
Deligne-Mumford, i.e. compactification of the space of mappings from a given
(wholly scheme like) curve, so, in particular, on quasi-projective projective
varieties. Under hypothesis on both the interior and the boundary such as
Remark \ref{rmk:interior} below, this implies an optimal logarithmic variant of
Mori's Bend-and-Break. The main technical remark is \ref{thm:logMM}, while our
final remark, the cone theorem, \ref{rmk:cone}, is a variant.
