  Using $\vec{k}$$\cdot$$\vec{p}$ theory, we derive an effective four band
model describing the physics of the typical two-dimensional topological
insulator (HgTe/CdTe quantum well) in the presence of out-of-plane in
z-direction inversion breaking and in-plane confining potentials. We find that
up to third order in perturbation theory, only the inversion breaking potential
generates new elements to the four band Hamiltonian that are off-diagonal in
spin space. When this new effective Hamiltonian is folded into an effective two
band model for the conduction (electron) or valence (heavy hole) bands, two
competing terms appear: (1) a Rashba spin-orbit interaction originating from
inversion breaking potential in z-direction and (2) an in-plane Pauli term as a
consequence of the in-plane confining potential. Spin transport in the
conduction band is further analysed within the Landauer-B\"uttiker formalism.
We find that for asymmetrically doped HgTe quantum wells, the behaviour of the
spin-Hall conductance is dominated by the Rashba term.
