We studied electric current and noise in planar GaN nanowires (NWs). The results obtained at low voltages provide us with estimates of the depletion effects in the NWs. For larger voltages, we observed the space-charge limited current (SCLC) effect. The onset of the effect clearly correlates with the NW width. For narrow NWs the mature SCLC regime was achieved. This effect has great impact on fluctuation characteristics of studied NWs. At low voltages, we found that the normalized noise level increases with decreasing NW width. In the SCLC regime, a further increase in the normalized noise intensity (up to 1E4 times) was observed, as well as a change in the shape of the spectra with a tendency towards slope -3/2. We suggest that the features of the electric current and noise found in the NWs are of a general character and will have an impact on the development of NW-based devices. ; Comment: 12 pages, 4 figures in Fluctuation and Noise Letters (2017)