  In this paper we present a classification of possible dynamics of closed
string moduli within specific toroidal compactifications of Type II string
theories due to the NS-NS tadpole terms in the reduced action. They appear as
potential terms for the moduli when supersymmetry is broken due to the presence
of D-branes. We particularise to specific constructions with two, four and
six-dimensional tori, and study the stabilisation of the complex structure
moduli at the disk level. We find that, depending on the cycle on the compact
space where the brane is wrapped, there are three possible cases: i) there is a
solution inside the complex structure moduli space, and the configuration is
stable at the critical point, ii) the moduli fields are driven towards the
boundary of the moduli space, iii) there is no stable solution at the minimum
of the potential and the system decays into a set of branes.
