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Tunnelling magnetoresistance (TMR) in polycrystalline Sr2FeMoO6 has been a matter of intense interest for more than a decade now, where the nature of the insulating tunnel barrier turned out to be the core issue of debate. Other than the nonmagnetic grain boundaries as conventional tunnel barriers, intragrain magnetic anti-phase boundaries (APB) as well as magnetically frustrated grain surfaces have also been proposed to act as tunnel barriers and influence the TMR response of Sr2FeMoO6 in different ways. In this paper, it is shown that depending upon the physical state of the sample, at least three different types of tunnelling mechanism may persist in polycrystalline Sr2FeMoO6 and a purely conventional TMR response, seldom reported in this important magnetoresistive material, is also possible.