We discuss the equilibrium shapes associated with complete wetting of two‐dimensional solids. We neglect effects due to incomplete wetting or disjoining pressure and argue that such neglect is a good approximation for a description of homogeneous, solid‐state sintering. The examples treated are building blocks for describing sintering processes. Analytical formulas are derived that describe the filling of various prototypical cavities which can be combined to yield extended realistic systems. The intricate consequences of the requirement of global equilibrium are discussed including questions of bridge formation and competition between different regions.

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