  In this letter we study topological open string field theory on D--branes in
a IIB background given by non compact CY geometries ${\cal O}(n)\oplus{\cal
O}(-2-n)$ on $\P1$ with a singular point at which an extra fiber sits. We wrap
$N$ D5-branes on $\P1$ and $M$ effective D3-branes at singular points, which
are actually D5--branes wrapped on a shrinking cycle. We calculate the
holomorphic Chern-Simons partition function for the above models in a deformed
complex structure and find that it reduces to multi--matrix models with
flavour. These are the matrix models whose resolvents have been shown to
satisfy the generalized Konishi anomaly equations with flavour. In the $n=0$
case, corresponding to a partial resolution of the $A_2$ singularity, the
quantum superpotential in the ${\cal N}=1$ unitary SYM with one adjoint and $M$
fundamentals is obtained. The $n=1$ case is also studied and shown to give rise
to two--matrix models which for a particular set of couplings can be exactly
solved. We explicitly show how to solve such a class of models by a quantum
equation of motion technique.
