In the advent of large-scale multi-hop wireless technologies, such as MANET, VANET, iThings, it is of utmost importance to devise efficient distributed protocols to maintain network architecture and provide basic communication tools. One of such fundamental communication tasks is broadcast, also known as a 1-to-all communication. We present a randomized algorithm that accomplishes broadcast in O (D +log(1/δ)) rounds with probability at least 1 - δ on any uniform-power network of n nodes and diameter D, when each station is equipped with its coordinates and local estimate of network density. Next, we develop algorithms for the model where no estimate of local density is available, except of the value n of the size of a given network. First, we provide a simple and almost oblivious algorithm which accomplishes broadcast in O (D log n(log n + log(1/δ))) rounds with probability at least 1 - δ . We further enhance this algorithm with more adaptive leader election routine and show that the resulting protocol achieves better time performance O ((D + log(1/δ)) log n) with probability at least 1 - δ. Our algorithms are the first provably efficient and well-scalable randomized distributed solutions for the (global) broadcast task in the ad hoc setting with coordinates. This could be also contrasted with the complexity of broadcast by weak devices, for which such scalable algorithms (with respect to D and log n) cannot be obtained .