Collision centrality for large heavy ion systems is well defined
both theoretically and experimentally, but the same is not necessarily
true when very asymmetric systems, like p/d+A, collide. In light of
some surprising result on the centrality dependence of high transverse
momentum observables in p/d+A collisions at RHIC and LHC,
the very concept of the geometrically inspired centrality gave way to
"event activity". Convincing experimental tests of the various
phenomenological models are so far missing. After a critical review of the
relevant results from SPS, RHIC and LHC we will discuss whether and how
the measurement of the ``centrality'' dependence of high and low
transverse momentum direct photons (pQCD and "thermal") in p/d+A
collisions, along with the photon/hadron ratios, can break the impass.
We will also explore whether there are any lessons to be learned with
respect to the possible formation of QGP droplets in small systems,
and extreme event classes in p+p and A+A collisions.