Self-Consistent Field Theory of Scheutjens and Fleer is extended to deal with highly branched polymer chains. Using the method, the surface adsorption and the steric stabilising properties of hydrophobically modified amylose and amylopectin were compared. For unmodified starch, both biopolymers induce attractive depletion interactions between emulsion droplets. However, for chains of comparable molecular weight, the forces are stronger and longer ranged for amylose. Upon hydrophobic modification, amylopectin has a higher level of surface adsorption, but forms thinner and denser interfacial layers. While both starch molecules provide a sufficient degree of steric repulsion to keep fine emulsions stable, those induced by amylose layers are longer ranged and decay more slowly with inter-droplet separation distances. This desirable property is partially offset by the greater propensity of linear chains to cause bridging. It is found that mixed layers of amylose and amylopectin lead to superior steric stabilising properties, as compared to either component alone.