Semiconductor nanowires with proximity-induced superconductivity are leading contenders for manifesting Majorana fermions in condensed matter1–5. However, unambiguous detection of these quasiparticles is controversial6, and one proposed method is to show that the peak in the conductance at zero applied bias is quantized to the value of 2e2/h (refs. 7–10). This has been reported previously11, but only by probing one end of the device. Yet, if peaks come from Majorana modes, they should be observed at both ends simultaneously. Here we fabricate devices that feature tunnel probes on both ends of a nanowire and observe peaks that are close to the quantized value. These peaks evolve with the tunnel barrier strength and magnetic field in a way that is consistent with Majorana zero modes. However, we only find nearly quantized zero-bias peaks localized to one end of the nanowire, while conductance dips are observed for the same parameters at the other end. We also identify delocalized states near zero magnetic field and at higher electron density, which is not in the basic Majorana regime. These results enable us to lay out procedures for assessing the non-locality of subgap wavefunctions and provide a classification of nanowire bound states based on their localization.Majorana bound states should appear at both ends of a nanowire if it is in the topological regime. This paper reports that, in many cases, zero-bias conduction peaks only occur on one end of the wire, which casts doubt on whether they are Majoranas.