  In this paper we study the behaviour of scalar flat K\"ahler ALE spaces and
their ADM mass under blow ups. In particular we prove that by blowing up
sufficiently many points at sufficiently big mutual distance one can produce
scalar flat metrics with arbitrarily large ADM mass. A general machinery for
producing scalar flat non Ricci flat ALE spaces of zero ADM mass is also
presented, using and integrating previous work by Rollin-Singer and
Hein-LeBrun.
