Because you said "deliver the same voltage" in terms of what sounds like the combination of batteries ("large"), it seems like you are talking about connecting the batteries in parallel. Connecting batteries in parallel will give you greater capacity at the same voltage (i.e. two batteries in parallel will deliver current to a load roughly twice as long as one battery, assuming the load impedance is much larger than the internal resistance of the batteries, and that the two batteries are of similar capacity.)
Connecting batteries in parallel will also increase their ability to deliver current. If the load is nearly the same as, or even less than, the internal resistance of the battery, then one battery may not be able to deliver sufficient current to the load, and, in fact, the voltage across the load will also be diminished (some of the voltage will be dropped across the batteries internal resistance). Adding one or more batteries in parallel will improve this--raising both the current and the voltage delivered.
You also need to consider if the conductors connecting the battery to the load are sufficient to deliver the required current without dropping significant voltage themselves.
So, in summary: the amount of current drawn from the battery(ies) is determined by the load. It doesn't matter how many batteries you connect in parallel, you will get the same current delivered to the same load, unless the impedance of the load is near the internal resistance of the battery, in which case more batteries in parallel will increase the current flow.
To develop 4.2v across a load such that 0.7 amps of current flows through that load--assuming DC--the load will need to be 4.2v/0.7A or 6 ohms. That's the law (Ohms law, to be exact)!
