A number of morphological and statistical aspects of domain formation in singly and doubly supported ternarymembranes have been investigated. Such ternary membranes produce macroscopic phase separation in two fluidphases and are widely used as raft models. We find that membrane interactions with the support surface can havea critical influence on the domain shapes if measures are not taken to screen these interactions. Combined AFM andfluorescence microscopy demonstrate small (500 nm) irregular domains and incomplete formation of much larger (5
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m) round domains. These kinetically trapped structures are the result of interactions between the membrane and thesupport surface, and they can be effectively removed by employing doubly supported membranes under physiologicalsalt concentrations. These decoupled supported membranes display macroscopic round domains that are easily perturbedby fluid shear flow. The system allows a quantitative characterization of domain coarsening upon being cooled intothe coexistence region. We determine the domain growth exponent
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= 0.31, which is in close agrement with thetheoretical value of 1/3. Analysis of the spatial domain pattern in terms of Voronoi polygons demonstrates a closesimilarity to equilibrated cellular structures with a maximized configurational entropy.