In this paper we present several set of solutions of static and spherically
    symmetric solitonic boson stars. Each set is characterized by the value of
    {\sigma} that defines the solitonic potential in the complex scalar field
    theory. The main features peculiar to this potential occur for small values of
    {\sigma}, but for which the equations become so stiff as to pose numerical
    challenges. Without making approximations we build the sets for decreasing
    {\sigma} values and show how they change their behavior in the parameter space,
    giving special attention to the region where thin-wall configurations dwell.
    The validity of the thin-wall approximation is explored as well as the
    possibility of the solution sets being discontinuous. We investigate five
    different possible definitions of a radius for boson stars and employ them to
    calculate the compactness of each solution in order to assess how different the
    outcomes might be.

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