Formation of the unique molecular species of mitochondrial cardiolipin requires tafazzin, a transacylase that exchanges acyl groups between phospholipid molecular species without strict specificity for acyl groups, head groups, or carbon positions. However, it is not known whether phospholipid transacylations can cause the accumulation of specific fatty acids in cardiolipin. Here, a model is shown in linear algebra representation, in which acyl specificity emerges from the transacylation equilibrium of multiple molecular species, provided that different species have different free energies. The model defines the conditions and energy terms, under which transacylations may generate the characteristic composition of mitochondrial cardiolipin. It is concluded that acyl-specific cardiolipin patterns could arise from phospholipid transacylations in the tafazzin domain, even if tafazzin itself does not have substrate specificity.