  Motivated by the fact that the Next-to-Minimal Supersymmetric Standard Model
is one of the most plausible models that can accommodate electroweak
baryogenesis, we analyze its phase structure by tracing the temperature
dependence of the minima of the effective potential. Our results reveal rich
patterns of phase structure that end in the observed electroweak symmetry
breaking vacuum. We classify these patterns according to the first transition
in their history and show the strong first-order phase transitions that may be
possible in each type of pattern. These could allow for the generation of the
matter-antimatter asymmetry or potentially observable gravitational waves. For
a selection of benchmark points, we checked that the phase transitions
completed and calculated the nucleation temperatures. We furthermore present
samples that feature strong first-order phase transitions from an extensive
scan of the whole parameter space. We highlight common features of our samples,
including the fact that the Standard Model like Higgs is often not the lightest
Higgs in the model.
