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We undertake an in-depth analysis of the magneto-transport properties in mesoscopic single-channel rings and multi-channel cylinders within a tight-binding formalism. The main focus of this review is to illustrate how the long standing anomalies between the calculated and measured current amplitudes carried by a small conducting ring upon the application of a magnetic flux $\phi$ can be removed. We discuss two different cases. First, we examine the combined effect of second-neighbor hoppingdoi:10.1515/ntrev-2012-0007 fatcat:7onjjvra6zdkpkeegdqcc2i62i