  This paper is to study cotorsion pairs and abelian model structures on some
Morita rings \ $\Lambda =\left(\begin{smallmatrix} A & {}_AN_B
  {}_BM_A & B\end{smallmatrix}\right)$. From cotorsion pairs $(\mathcal U,
\mathcal X)$ and $(\mathcal V, \mathcal Y)$, respectively in $A$-Mod and
$B$-Mod, one constructs 4 kinds of cotorsion pairs in $\Lambda$-Mod. There even
exists an algebra $\Lambda$ such that the four cotorsion pairs above are
pairwise different. The heredity and completeness of these cotorsion pairs are
studied. The problem of identifications, namely, when the first two cotorsion
pairs are the same, and when the second two cotorsion pairs are the same, is
investigated. Various model structures on $\Lambda$\mbox{-}{\rm Mod} are
obtained, by explicitly giving the corresponding Hovey triples and Quillen's
homotopy categories. In particular, cofibrantly generated Hovey triples, and
the Gillespie-Hovey triples induced by compatible generalized projective
(respectively, injective) cotorsion pairs, are explicitly contructed.
