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We have investigated the lateral distributions of critical current densities in narrow coated conductors slit by different cutting methods. The objective was to find an optimal slitting process to make a narrow conductor that should be effective for ac loss reduction of assembled conductors such as power transmission cables. In-plane 2-D distribution of critical current density was characterized by means of scanning Hall-probe microscopy. From an analysis along the width direction, we could estimate the degradation in critical current density by a slitting process at both tape edges. We determined an equivalent width for the slit tapes in order to discuss such degradation with a high spatial resolution. Furthermore, the 2-D scanning allows us to evaluate the effective tape width as a function of longitudinal coordinate. In other words, we could evaluate the equivalent width of a slit conductor together with its statistics along the longitudinal direction. As a result, it was found that coated conductors slit by laser cutting processes were clearly better than those by mechanical ones from the viewpoint of less degradation at their edges. In addition, an optimal condition among laser slitting processes was also presented.