  Perhaps the best understood phase transition is that in the component
structure of the uniform random graph process introduced by Erd\H{o}s and
R\'enyi around 1960. Since the model is so fundamental, it is very interesting
to know which features of this phase transition are specific to the model, and
which are `universal', at least within some larger class of processes (a
`universality class'). Achlioptas process, a class of variants of the
Erd\H{o}s--R\'enyi process that are easy to define but difficult to analyze,
have been extensively studied from this point of view. Here, settling a number
of conjectures and open problems, we show that all `bounded-size' Achlioptas
processes share (in a strong sense) all the key features of the
Erd\H{o}s--R\'enyi phase transition. We do not expect this to hold for
Achlioptas processes in general.
