Copper sheathing was introduced at about the time of the American Revolution. (The first experiments with it seem to have taken place about 1750; during the War of American Independence, British warships got coppered as they went into drydock for refits.) By the time of the French Revolution virtually all major warships of the major navies had copper bottoms.
Prior to the introduction of copper sheathing a number of treatments were used that (it was hoped) retarded marine growth and boring worms on ships' bottoms. The materials used included horsehair, tar, pitch, sulphur, rosin, tallow, white lead paint, and "train oil" (whatever that is). The treatments were generally categorized as "white stuff," "black stuff," and "brown stuff," with "black stuff" probably being the most common. (My source on this is the section on hull sheathing in the relevant volume of the Conway's History of the Ship series, The Line of Battle: The Sailing Warship, 1650-1840.) I can't recall having bumped into a reference to lime being used in such a concoction, but I guess it's possible.
I've also never heard the pieces of copper used in metal sheathing referred to as "tiles," but they were indeed applied (generally speaking) in tile fashion. In fact they were extremely thin sheets of copper (later with tin and/or zinc mixed in), usually measuring about 14" x 48" (the size varying from nation to nation and from time to time). The thickness varied according to the part of the ship to which the sheathing was applied, with the bow and waterline areas getting the thickest. According to George Campbell's China Tea Clippers, the thickness of the sheets in the early nineteenth century varied from .025" to .044". On a model of any but the largest scale, the difference is negligible.
The sheets were put on with nails (about sixty nails per plate, according to Mr. Campbell), and overlapped each other by about an inch. (Whether each row overlapped the one above or the one below is a matter of some discussion; in practice, it probably wasn't consistent, especially when an older ship got re-coppered.)
Scratchbuilders often represent copper sheathing with sheets of .001" thickness or less - still too thick for exact scale, but not conspicuously so. Plastic sailing ship kit manufacturers trying to represent copper sheathing have a decision to make. Revell and Heller usually made a valiant attempt to represent the overlap at the edges of the plates, by depicting them in relief. Strictly speaking that was overdone, but to many eyes (including mine) pretty effective. (Revell also did a remarkably good job of representing the nail heads. Heller didn't - even in its big H.M.S. Victory.) In at least one of its kits, the yacht America (released in 1969, as one of the company's last genuinely new sailing ship kits - when the firm was having some big financial problems) Revell represented the edges of the copper sheets with raised lines. And a couple of companies, Airfix (in its H.M.S. Bounty) and Aurora, represented them with countersunk lines. If I remember correctly, that's how the sheathing on the Wanderer kit is represented.
In strict scale terms, all of those techniques are wrong. In a 1/96-scale model of a ship sheathed with, say, .044" copper sheets, the scale thickness of the overlap would be .0004583". (That's less than five ten-thousandths of an inch. The typical human eye would have a hard time detecting it.) It could be argued that the most accurate way to represent a copper-hulled ship is to give it a smooth bottom. Many modelers (including me) argue, though, that the impression of the copper sheathing is more important than the precise scale dimensions. I personally wouldn't regard a smooth-bottom on a model of a copper-sheathed ship (except on a very small scale) as very convincing.
Since any of the alternatives is technically wrong, the choice between them really boils down to personal taste. Donald McNarry, whose models on very small scales are generally regarded as being among the best in the world, lays his copper sheets edge-to-edge, with no overlap. To my eye the results look terrrific (if more than slightly humiliating). To my eye the "falsely-overlapping" sheets provided by Heller and Revell also look good; their appearance certainly can be enhanced by a good, careful job of weathering. And the approach taken by Aurora on that old whaler kit (scribed lines representing the plate edges) certainly strikes me as being just as legitimate as any other.
Modelers sometimes forget (or try to ignore) the extent to which they are in fact presenting a visual impression of reality rather than reproducing it precisely to scale. (How many modelers have ever bothered to consider how thick the plating of a 40mm gun tub really should be on 1/700 scale battleship? Or how thick a landing gear door should be on a 1/72 scale airplane?) It's fairly safe to assert, I think, that almost no ship model is 100 percent to scale. (About the only exception I can think of is the model of the whaler Lagoda in the New Bedford Whaling Museum. It's on 1/2 scale. Not 1/2" = 1' - one-half actual size.) The representation of copper sheathing is just one of many examples.