  The Tolman--Oppenheimer--Volkoff (TOV) equations are a partially uncoupled
system of nonlinear and non-autonomous ordinary differential equations which
describe the structure of isotropic spherically symmetric static fluids.
Nonlinearity makes finding explicit solutions of TOV systems very difficult and
such solutions and very rare. In this paper we introduce the notion of
pseudo-asymptotic TOV systems and we show that the space of such systems is at
least fifteen-dimensional. We also show that if the system is defined in a
suitable domain (meaning the extended real line), then well-behaved
pseudo-asymptotic TOV systems are genuine TOV systems in that domain, ensuring
the existence of new fourteen analytic solutions for extended TOV equations.
The solutions are classified according to the nature of the matter (ordinary or
exotic) and to the existence of cavities and singularities. It is shown that at
least three of them are realistic, in the sense that they are formed only by
ordinary matter and contain no cavities or singularities.
