we present the boundary and initial conditions, introduce the main notation, nondimensionalise the main equations, state the stationary equation for the density, define the weak formulation of the Smoluchowski equation including full HI and provide a list of assumptions. In Section \[sec:statement\_of\_main\_results\] we state the main results of the present work in a precise manner. In Section \[sec:ex\_uni\_full\_HI\] we provide an existence and uniqueness theorem for the flux $\vec{a}$ when full HI are included. In Section \[sec:char\_stationary\_sol\] we characterise solutions of the stationary problem and convergence to equilibrium in $L^2$ as $t \to \infty$. In Section \[sec:global\_asymptotic\_stability\] we obtain results on the global asymptotic stability of the stationary densities by showing that the free energy is a continuous functional for all two-body interaction strengths. Additionally we prove an H- theorem for the equilibria, provide *a priori* convergence estimates in relative entropy, derive an asymptotic expansion of the equilibria for small interaction energy and perform a spectral analysis of the linearised nonlocal Smoluchowski operator. In Section \[sec:bifurcation\_theory\] we provide necessary and sufficient conditions for phase transitions in generalised DDFT-like systems with no-flux boundary conditions. In Section \[sec:manufactured\_bif\] we construct the bifurcation diagram for some example problems. In Section \[sec:existence\_uniqueness\_with\_partial\_HI\] we obtain 