A system for sensing multiple local electric voltages from endocardial surface of a heart, comprising: an elongate tubular member having a lumen, a proximal end and a distal end; a plurality of flexible splines having proximal portions, distal portions and medial portions therein between, wherein the splines comprise an outer surface, an inner surface and two side surfaces (194, 195); an anchor having an open lumen and spline-receiving slots on an exterior portion for securably affixing the proximal portions of the splines, wherein the anchor is securably affixed within the lumen of the elongate tubular member at the distal end of the elongate tubular member; a distal tip for affixing the distal portions of the splines; and a polymeric member comprising opposed a first open end and a second open end defining an open lumen therein between and an inner member surface and an outer member surface, wherein at least one of the plurality of flexible splines is at least partially disposed within the lumen of said polymeric member; a flexible electrode assembly strip having a proximal portion, a medial portion and a distal portion, the medial and distal portions having with one or more exposed electrodes disposed on at least a portion of the outer surface of said polymeric member; wherein the flexible electrode assembly strip comprises: a polymeric substrate having an inner surface and an opposed outer surface; said one or more exposed electrodes disposed over at least part of the outer surface of the polymeric substrate; and one or more electrical traces disposed over at least a portion of the inner surface of the polymeric substrate or over at least a portion of the outer surface of the polymeric substrate, said one or more electrical traces being in electrical communication with said one or more exposed electrodes; wherein the proximal a portion of the flexible electrode assembly transitions from the outer surface of said polymeric member towards the inner surface of said polymeric member prior to said anchor and extends through the open lumen of said anchor and into said lumen of said elongate tubular member. an elongate tubular member having a lumen, a proximal end and a distal end; a plurality of flexible splines having proximal portions, distal portions and medial portions therein between, wherein the splines comprise an outer surface, an inner surface and two side surfaces (194, 195); an anchor having an open lumen and spline-receiving slots on an exterior portion for securably affixing the proximal portions of the splines, wherein the anchor is securably affixed within the lumen of the elongate tubular member at the distal end of the elongate tubular member; a distal tip for affixing the distal portions of the splines; and a polymeric member comprising opposed a first open end and a second open end defining an open lumen therein between and an inner member surface and an outer member surface, wherein at least one of the plurality of flexible splines is at least partially disposed within the lumen of said polymeric member; a flexible electrode assembly strip having a proximal portion, a medial portion and a distal portion, the medial and distal portions having with one or more exposed electrodes disposed on at least a portion of the outer surface of said polymeric member; wherein the flexible electrode assembly strip comprises: a polymeric substrate having an inner surface and an opposed outer surface; said one or more exposed electrodes disposed over at least part of the outer surface of the polymeric substrate; and one or more electrical traces disposed over at least a portion of the inner surface of the polymeric substrate or over at least a portion of the outer surface of the polymeric substrate, said one or more electrical traces being in electrical communication with said one or more exposed electrodes; a polymeric substrate having an inner surface and an opposed outer surface; said one or more exposed electrodes disposed over at least part of the outer surface of the polymeric substrate; and one or more electrical traces disposed over at least a portion of the inner surface of the polymeric substrate or over at least a portion of the outer surface of the polymeric substrate, said one or more electrical traces being in electrical communication with said one or more exposed electrodes; wherein the proximal a portion of the flexible electrode assembly transitions from the outer surface of said polymeric member towards the inner surface of said polymeric member prior to said anchor and extends through the open lumen of said anchor and into said lumen of said elongate tubular member.