<p><b>Abstract</b>—We consider the problem of broadcasting multiple messages from one processor to many processors in the <tmath>$k$</tmath>-port model for message-passing systems. In such systems, processors communicate in rounds, where in every round, each processor can send <tmath>$k$</tmath> messages to <tmath>$k$</tmath> processors and receive <tmath>$k$</tmath> messages from <tmath>$k$</tmath> processors. In this paper, we first present a simple and practical algorithm based on variations of <tmath>$k$</tmath> complete <tmath>$k$</tmath>-ary trees. We then present an optimal algorithm up to an additive term of one for this problem for any number of processors, any number of messages, and any value for <tmath>$k$</tmath>.</p>