IPTV systems attracting millions of users are now commonly deployed on peer-to-peer (P2P) infrastructures and provide an appealing alternative to multicast-based systems. Typically, a P2P overlay network is associated with each channel, composed of users who receive, watch and redistribute this channel. Yet, channel surfing (aka as zapping) involves switching overlays and may introduce delays, potentially hurting the user experience when compared to multicast-based IPTV. In this paper, we present a distributed system called OAZE (Overlay Augmentation for Zapping Experience) which speeds up the switching process and reduces the overall cross-domain traffic generated by the IPTV system. In OAZE, each peer maintains connections to other peers, not only in a given channel, but also in a subset of all channels to which the associated user is likely to zap. More specifically, we focus on the channel assignment problem,i.e.determining, in a given P2P overlay, the optimal distribution of the responsibility to maintain contact peers to other channels. We propose an approximate algorithm providing guaranteed performances, and a simpler and more practical one. Our experimental results show that OAZE leads to substantial improvements on the connections between peers, resulting in less switching delay and lower network cost; it then represents an appealing add-on for existing P2P IPTV systems.