Microtubule organization is key to eukaryotic cell structure and function. In most animal cells, interphase microtubules organize around the centrosome, the major microtubule organizing centre (MTOC). Interphase microtubules can also become organized independently of a centrosome, but how acentrosomal microtubules arrays form and whether they are functionally equivalent to centrosomal arrays remains poorly understood. Here, we show that the interphase microtubule arrays of fission yeast cells can persist independently of nuclear-associated MTOCs, including the spindle pole body (SPB)--the centrosomal equivalent. By artificially enucleating cells, we show that arrays can form de novo (self-organize) without nuclear-associated MTOCs, but require the microtubule nucleator mod20-mbo1-mto1 (refs 3-5), the bundling factor ase1 (refs 6,7), and the kinesin klp2 (refs 8,9). Microtubule arrays in enucleated and nucleated cells are morphologically indistinguishable and similarly locate to the cellular axis and centre. By simultaneously tracking nuclear-independent and SPB-associated microtubule arrays within individual nucleated cells, we show that both define the cell centre with comparable precision. We propose that in fission yeast, nuclear-independent, self-organized, acentrosomal microtubule arrays are structurally and functionally equivalent to centrosomal arrays.