  We investigate the phenomenom of emerging regular spectral features from
random interactions. In particular, we address the dominance of L=0 ground
states in the context of the vibron model and the interacting boson model. A
mean-field analysis links different regions of the parameter space with
definite geometric shapes. The results that are, partly, obtained in closed
analytic form, provide a clear and transparent interpretation of the
distribution of ground state angular momenta as observed before in numerical
studies.
