This paper analyzes how TCP congestion control can propagate self-similarity between distant areas of the Internet. This property of TCP is due to its congestion control algorithm, which adapts to self-similar fluctuations on several timescales. The mechanisms and limitations of this propagation are investigated. It is demonstrated that if a TCP connection shares a bottleneck link with a self-similar background traffic flow, it propagates the correlation structure of the background traffic flow asymptotically, above a characteristic timescale. The cut-off timescale depends on the end-to-end path properties, e.g. round-trip time and average window size, and the receiver window size in case of high-speed connections. It is also shown that even short TCP connections can propagate long-range correlations effectively. In case when TCP encounters several bottleneck hops, the end-user perceived end-to-end traffic is also long-range dependent and it is characterized by the largest Hurst exponent. Through simple examples, it is shown that self-similarity of one TCP stream can be passed on to other TCP streams that it is multiplexed with. The limitations of propagation depend on network conditions. Propagation complements the widespread scaling phenomena reported in the literature. Our arguments are supported with a combination of analytic techniques, simulations and statistical analyzes of a number of wide area Internet traffic measurements.