This paper explores the spatial multiplexing gain in a relay assisted distributed wireless network, where multiple relays, each with a single antenna, form a virtual antenna array to transmit to a receiver with multiple antennas. Using a transmission scheme called Randomized Distributed Spatial Multiplexing (RDSM), the transmission rate between the relays and the destination is boosted to a level that is several times higher than the rate that can be achieved through a single relay. As a result, the end-to-end data rate between a source and a destination can be greatly improved. Consequently, in a wireless network, where multiple sources compete for channel access, the overall system aggregated throughput is also improved. An opportunistic rate adaptation algorithm is adopted to achieve the optimal average end-to-end performance. Randomized signal processing at the relays fundamentally changes the way how cooperation is established. Instead of picking nodes with good links or fast paths, our algorithm picks a transmission mode (modulation, coding, and number of streams). Any node that correctly receives from the source can act as a relay and participate in forwarding. We present the performance of RDSM with practical modulation and channel coding, and evaluate its performance in a fully distributed wireless scenario.