  In this paper we give a characterisation of real closure * of regular rings,
which is quite similar to the characterisation of real closure * of Baer
regular rings seen in [4]. We also characterize Baer-ness of regular rings
using near-open maps. The last part of this work will concentrate on
classifying the real closure * of Baer and non-Baer regular rings (upto
isomorphisms) using continuous sections of the support map, we construct a
topology on this set for the Baer case. For the case of non-Baer regular rings,
it will be shown that almost no information of the ring structure of the Baer
hull is necessary in order to study the real and prime spectra of the Baer
hull. We shall make use of the absolutes of Hausdorff spaces in order to give a
construction of the spectra of the Baer hulls of regular rings. Finally we give
example of a Baer regular ring that is not rationally complete.
