Tidal hydrokinetic power generation involves the conversion of the kinetic power in swiftly moving tidal currents to renewable electricity. Resource assessment is critical to understand the tidal hydrokinetic potential, but is complicated by a number of factors, including far-field effects. These are changes to the tidal regime caused by the increased resistance to flow as power is extracted from a channel network. This study addresses far-field effects in four prototypical channel networks: multiply-connected flow around an island, a branching network in which the flow bifurcates but does not converge downstream, and a network with multiple constrictions in series. These networks are modeled as one-dimensional channels with hydrokinetic power extraction in high current constrictions. Changes to tides, transport, frictional power dissipation, and kinetic power density are quantified for a range of extraction options. Depending on the type of network, the tidal regime may be either locally augmented or reduced by kinetic power extraction. The changes to kinetic power density throughout the network have important implications for resource assessment, particularly for networks with multiple extraction sites. Results suggest that existing analytical methods tend to over- or under-estimate the hydrokinetic resource because they do not allow for changes to the tidal forcing as a consequence of extraction. In general, site-specific numerical modeling is required to quantitatively predict far-field extraction effects and assess the hydrokinetic resource.