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We have studied Co/Cu multilayers to understand the effect of the sample's width on their magneto-resistance (MR). By keeping constant both the length and the thickness and exploring the widths within the range of usual magnetic domain sizes in those nanostructures, we were able to observe effects on the MR curve, as well as infer linked changes in the magnetization process. Associating MR and Planar Hall Effect (PHE) measurements, coupled to an analysis of the MR plots' symmetry, we were able to establish that, apart from the expected antiferromagnetic coupling, reducing the width forces the magnetization to stay aligned to the current channel, thus inducing more symmetric, closer to model Giant Magnetoresistance (GMR). Also, the sample edges might contribute by adding extra coupling through magnetostatic interaction. The added effects result in a counter-intuitive trend that goes from the near ideal wide samples through intermediate sizes with fairly abrupt changes in MR, and finally to the closer to bell-shaped ideal GMR at narrow widths. [ABSTRACT FROM AUTHOR]