Context. The morphology of spectral line polarization is the most valuable observable to investigate the magnetic and dynamic solar atmosphere. However, in order to develop solar diagnosis, it is fundamental to understand the different kinds of anomalous solar signals that are routinely found in linear and circular polarization (LP,CP). Aims: We aim to explain and characterize the morphology of solar CP signals considering nonlocal thermodynamical equilibrium (NLTE) effects. Methods: An analytical two-layer model of the polarized radiative transfer equation is developed and used to solve the NLTE problem with atomic polarization in a semi-parametric way. The potential of the model for reproducing anomalous CP is shown with detailed calculations and examples. A new approach based on the zeroes of polarization signals is developed to explain their morphology. Results: We have obtained a comprehensive model that insightfully describes the formation of solar polarization with certain precision without sacrificing key physical ingredients or resorting to complex atmospheric models. The essential physical behavior of dichroism and atomic orientation has been described, introducing the concepts of dichroic inversion, neutral and reinforcing medium, critical intensity spectrum, and critical source function. We show that the zero-crossings of the CP spectrum are useful to classify its morphology and understand its formation. This led to identification and explanation of the morphology of the seven most characteristic CP signals that a single (depth-resolved) scattering layer can produce. We find that a minimal number of two magnetic layers along the line of sight is required to fully explain anomalous solar CP signals and that the morphology and polarity of Stokes V depends on magnetic, radiative, and atomic "polarities". Some implications of these results are presented through a preliminary modeling of anomalous CP signals in the Fe I 1564.8 nm and Na I D lines.