The research interest in sensor nets is still growing because they simplify data acquisition in many applications. If hardware resources are very sparse, routing algorithms cannot use data gathering. However, if a large number of channels can be used, then parallel transmission can compensate this drawback. If the senders and receivers are not known in advance, then a control channel poses a bottleneck for communication. We present an oblivious MAC protocol, called the Funnel protocol, where the channels are nearly optimally utilized in parallel. In this, senders and receivers choose for a polylogarithmic number of rounds (several sending attempts) a decreasing number of channels which are selected equiprobably. Then, we show that a previously presented approach using only one round and therefore one type of probability distribution is optimal up to some constant factor, and considerably worse than the Funnel protocol. The protocol works with few resources if an sufficient number of ...