Monte Carlo (MC) simulations combined with the constant bond energy (CBE) model are set up to explore and understand the general segregation behaviour in ternary alloys as a function of composition and more in particular the segregation to Cu-Ni-Al (100) surfaces. Besides its simplicity, allowing swift simulations, which are necessary for a first general survey over all possible compositions, one of the advantages of the CBE model lies in the possibility to clearly identify the different driving forces for segregation. All simulations are pet-formed in the Grand Canonical Ensemble, using a new algorithm to determine the chemical potential of the components. Notwithstanding the simplicity of the CBE model, one extra feature is evidenced: depending on the values of the interatomic interaction parameters, in some regions of the ternary diagram, a single solid solution becomes thermodynamically unstable, leading to demixing into two conjugate phases. The simulations are first done for three hypothetical systems that are however representative for real alloy systems. The three systems are characterised by different sets of interatomic interaction parameters. These extensive simulations over the entire composition range of the ternary alloy yield a "topographical" segregation map, showing distinct regions where different species segregate. These distinct domains originate from a variable interplay between the driving forces for segregation and attractive/repulsive interactions in the bulk of the alloy. The results on these hypothetical systems are very helpful for a better understanding of the segregation behaviour in Cu-Ni-Al and other ternary alloys. (C) 2003 Elsevier Science B.V. All rights reserved.