Where does the water from rain in rain forests come from?
Leaves, mostly. Photosynthesis requires carbon dioxide, and it gets it via stomata - small controllable pores in the leaf. When the stomata open, water goes out, because the air is generally drier than the interior of the leaf. Water in the leaves is drawn up from the roots, via the xylem, using the suction from the lost water in the leaves, and also acting as a capillary.

As for how much water comes from transpiration, Brustaert (2005) includes a list of estimates of global annual evapotranspiration from the land that range from 0.42-0.54 my$^{-1}$ (averaged over all 1.49×10$^8$ km$^2$), and 1.18-1.4 my$^{-1}$ for the ocean (3.61×10$^8$ km$^2$). That 6.22×10$^{13}$-7.99×10$^{13}$ tonnes of water or 62.2-79.9 petatonnes, compared to 425-505 petatonnes for the ocean.

So, for Earth, the land is something like an sixth of the total evaporation. Keep in mind that that includes desert areas. A rainforest planet would have significantly higher evaporation than that, per square meter. For example, Malhi et al. (2002) calculate evapotranspiration over the rainforest in the Amazon at 1.12 my$^{-1}$. That is much closer to ocean rates than average land rates. 


Brutsaert, W., 2005. Hydrology: An Introduction, Cambridge University Press.
Malhi, Y. et al., 2002. Energy and water dynamics of a central Amazonian rain forest. Journal of Geophysical Research: Atmospheres, 107(D20), p.8061.