The Kyrgyz Range, located on the northern margin of the western Tian Shan, illustrates long-term (10⁶–10⁷ year) transient landscape evolution in response to an active basement-cored rock uplift. Eastward propagation of range uplift has progressively exposed resistant bedrock capped by a tilted, (formerly) planar, pre-Cenozoic unconformity. We develop an approximate, stream power–based analytic model of transient river profile incision into progressively exposed and resistant bedrock to explore the patterns of channel development into the unconformity surface. This analysis shows that the unconformity can be preserved as a geomorphic marker defined by upland headwaters and interfluvial areas. Though channels are not at equilibrium with rock uplift, prominent knickpoints are not predicted to develop on main stem channels. However, knickpoints are predicted to develop on tributaries upstream of their junctions with the trunk stream because of differential erosion rates. Initial channel slope and transient channel form are both sensitive to the n value of the stream power model and could prove useful for calibration of n from field data. Accumulation of catchment area (a proxy for discharge) into larger catchments develops a positive feedback where larger drainages with higher stream power at a given slope undermine and capture adjacent drainage area. A simple model of competitive fluvial incision illustrates the role of tributary junction position in maximizing stream power expended upon the trunk stream. Examples from the Kyrgyz Range illustrate the effects of tributary junction position on fluvial relief, and we propose that adjustments to the tributary network through stream capture are ongoing within this landscape even after several kilometers of exhumation.