Using mesoscopic interfacial models and microscopic density functional theory we study fluid ad-sorption at a dry wall decorated with three completely wet stripes of widthLseparated by distancesD1andD2. The stripes interact with the fluid with long-range forces inducing a large finite-sizecontribution to the surface free-energy. We show that this non-extensive free-energy contributionscales with lnLand drives different types of bridging transition corresponding to the merging ofliquid drops adsorbed at neighbouring wetting stripes when the separation between them ismolecu-larlysmall. We determine the surface phase diagram and show that this exhibits two triple points,where isolated drops, double drops and triple drops coexist. For the symmetric case,D1=D2≡D,our results also confirm that the equilbrium droplet configuration always has the symmetry of thesubstrate corresponding to either three isolated drops whenDis large or a single triple drop whenDis small; however, symmetry broken configurations do occur in a metastable part of the phasediagram which lies very close to the equilibrium bridging phase boundary. Implications for phasetransitions on other types of patterned surface are considered.