Wart formation is actually the way HPV spreads to surrounding tissue. The virus itself infects a cell, replicates and spreads to neighboring cells that are in direct contact with the infected cell. These cells replicate and grow in an uncontrolled manner, and this is how the wart tumor is formed.
The wart itself, is not uniform throughout. The top layer of the wart is dry, and more easily flakes off. This infected skin that flakes off is able to create new warts if it flakes off and enters somewhere else in the anogenital area, through the top layer of skin (usually through abrasions, cuts, scrapes, etc.).
This is the mode of transmission that HPV has evolved to help propagate itself and spread throughout a host's/host's sexual partner's skin.
If you have no visible warts, you have a smaller chance of spreading the virus through the aforementioned flaking of dry, infected skin.
However, the virus is able to live in normal looking skin without producing a wart. If this normal-looking, but infected skin containing virus particles comes in contact with the lower layers of skin, there is a possibility the virus particle will enter into a new cell, and infect it, and possibly lead to the formation of a wart (or lay dormant).
Clearly, it's hard to speak in absolutes concerning HPV transmission.
The general consensus is that 6 months without any wart formation is enough to say your immune system has either completely eliminated the infection, or reduced it to undetectable levels. Of course, there are some people who will go 10 years without symptoms only to have warts pop up. There are always exceptions in medicine, but again - 6 months with no warts, it is most likely safe to assume you are unlikely to transmit the virus.
Sorry if this was long, I'm just in an informative mood.