It’s been said you could build a large house out of all the little wood chips and splinters of the cross in cathedrals all over Europe.
Its been said by a quipping skeptic... and I think it was "a large barn"... and another went whole hog claiming "...the cathedral from the pieces"... but its not factual.
A volumetric inventory of ALL of the know pieces of the "True Cross" was undertaken several decades ago by a Catholic priest with an engineering degree who made a years long pilgrimage to examine every confirmed cross relic. Precise measurements were taken of each surviving piecethey seem to be the same species of acacia woodno matter how small. The various pieces varied in size from splinters to one over ten inches in length. The total volume calculated shows there is enough wood to make up about two-thirds of a standard Roman patibulum, the horizontal cross piece to which the arms/hands would be nailed. That would be a beam of wood about ~6.5 to ~7 long by ~6" wide by ~4" to ~6" thick.
The stapes, the upright post, was normally permanently installed and re-used for multiple executions. It might or might not have a sedulous, a cross plank to sit on, and/or a pedula, an angled piece of wood for nailing the feet on. A titulus, a written indictment of the criminals crime(s), could be either affixed on the stapes above the patibumum, or if on a tau cross (T shaped), on a stick stuck on top. A portion of the middle of Jesus Titulus is thought to survive to this day, having been cut into pieces in the first millennia for unknown reasons and distributed. The piece is about one-third of the original titulus. .
One thing that tends to lead to the authenticity to the Jesus Titulus is that both the Latin and Greek language indictments are carved into the wood in the same right to left direction as the Hebrew right to left script of the first line is. A C14 test on a very small splinter of the Titulus wood dated it to early first century.