A catheter adapted or high density mapping and/or ablation of tissue surfacehas a distalelectrode matrix having a plurality of spines arranged in parallelconfiguration on which amultitude of electrodes are carried in a grid formation for providinguniformity andpredictability in electrode placement on the tissue surface. The matrix can bedragged againstthe tissue surface upon deflection (and/or release of the deflection) of thecatheter. The spinesgenerally maintain their parallel configuration and the multitude ofelectrodes generallymaintain their predetermined relative spacing in the grid formation as thematrix is draggedacross the tissue surface in providing very high density mapping signals. Thespines may havefree distal ends, or distal ends that are joined to form loops for maintainingthe spines inparallel configuration.