*After looking at all of the comments, this is my personal conclusion for the ultimate "world tree". *
 **Leaves with very short hairs.** These leaves would not only produce energy through photosynthesis but absorb water like roots, where the hairs act as root hairs. With slightly different physiology this is certainly possible.
 **Location in a valley providing relative shelter from winds.** The tree would also be very thick at the bottom and get progressively thinner to avoid breaking.
 **No more than 2000 meters (2 km) high to avoid constant, ultra-low temperatures, but still have a massive size.** This would also remove the need to make ridiculously strong wood or other, more complicated and/or unrealistic elements.
 **Light but relatively strong wood.** The tree would also (as with most plants) have a high lignin content, from which it would somehow produce its own carbon fibre and implement it into its own structure in high quantities, greatly strengthening the tree to keep it from essentially imploding.
 **Pools of water from interlocking branches and/or leaves above ground-level, drawing in critters and providing energy reserves if needs be.** Microbes, insects, small mammals, and other organisms would be attracted to the relative safety/shelter of the tree, and with water, they would be even more likely to wish to take up refuge there. They could provide minerals and other nutrients in the form of their waste, and could even form a stronger symbiotic relationship of some kind (use your imagination). The pools would also work as energy stores, where the water could be saved and then used by the water-absorbent leaves.
 **Very thin channels in the tree.** Water and other nutrients could travel throughout the tree based simply on the behaviour of fluids in very small channels (see Jesse Williams’ response for a somewhat more detailed description).
 **Large root system capable of bringing other nutrients and support/stability.**