What underlies the right hand advantage that is evident in the majority of the population? It is probably safe to assume that the manual asymmetry is reflection of the inherent capabilities of each hemisphere - some have suggested that the left hemisphere is specialized for sending accurate motor commands to the limbs, that need little in the way of correction.
Evidence for this proposition is rather mixed however. Perhaps some cerebral asymmetry drives selection of the right hand in the majority of the population. Or, more interestingly, the right hand is assigned the more complicated portion of a bimanual task. Consider the different challenges required by either hand when opening a bottle of water, or buttoning a shirt - one hand's task is to stabalise, while the other gets assigned the more attentionally demanding task. But what drives this bias toward selecting the right hand for the complex portion of bimanual tasks?
Michael Peters, following an imaginative series of experiments in the 1980's and 90's, suggested that the simplest explanation may be that attention is biased toward the right hand of right-handers. This attentional bias (possibly stemming from a rightward head-turnining bias in infancy) is likely to drive selection biases during bimanual coordination, and crucially, become apparent during tasks involving the concurrent use of both hands.
I examined this topic in great detail during my graduate studies. I initially examined a rythmic bimanual coordination task (wiggling the index fingers together out-of-time), while the hands were separated by a mirror. As this paradigm yeilded no obvious asymmetries, I shifted the direction of my research toward goal-directed bimanual reaches - more akin to the coordination that is a feature of early ontonological development. In several experiments involving the use of double-step reaching, cueing, and hemispatial asymmetries, I was able to demonstrate some evidence of a bias in attention toward the dominant hand. Details of these individual experiments can be found in the publications and presentations sections. If you would like to see my PhD thesis for the excessively detailed stuff, feel free to contact me.