  The purpose of this note is to prove that there is an algebraic stack U
parameterizing all curves. The curves that appear in the algebraic stack U are
allowed to be arbitrarily singular, non-reduced, disconnected, and reducible.
We also prove the boundedness of the open substack of U parameterizing
geometrically connected curves with fixed arithmetic genus g and $\leq$ e
irreducible components. This is an updated and expanded version of
[arXiv:0902.3690v2, Appendix B].
