Mitochondria are highly dynamic organelles, containing vital populations of mitochondrial DNA (mtDNA) distributed throughout the cell. Mitochondria form diverse physical structures in different cells, from cell-wide reticulated networks to fragmented individual organelles. These physical structures are known to influence the genetic makeup of mtDNA populations between cell divisions, but their influence on the inheritance of mtDNA at divisions remains less understood. Here, we use statistical and computational models of mtDNA content inside and outside the reticulated network to quantify how mitochondrial network structure can control the variances of inherited mtDNA copy number and mutant load. We assess the use of moment-based approximations to describe heteroplasmy variance and identify several cases where such an approach has shortcomings. We show that biased inclusion of one mtDNA type in the network can substantially increase heteroplasmy variance (acting as a genetic bottleneck), and controlled distribution of network mass and mtDNA through the cell can conversely reduce heteroplasmy variance below a binomial inheritance picture. Network structure also allows the generation of heteroplasmy variance while controlling copy number inheritance to sub-binomial levels, reconciling several observations from the experimental literature. Overall, different network structures and mtDNA arrangements within them can control the variances of key variables to suit a palette of different inheritance priorities. Author summary In many organisms, mitochondria form large, connected networks. The reasons for this network formation are not fully understood, and it is likely that several different advantages may be provided by a physical network structure. Here we use maths and simulation to show and explore one of these possible advantages. By forming physical networks in the cell, mitochondria can control the inheritance of the vital mtDNA molecules that they contain. Different physical behaviour of mitochondrial networks can both generate useful variability in, and tightly control, the genetic mtDNA content of daughter cells after divisions. This physical control of genetic content allows different priorities to be addressed, including the segregation of mutational damage, and the faithful inheritance of mtDNA copy number.