I have been research the topic of how Christ died and have read many articles (most interesting of them was at the URL http://www.freeminds.org/doctrine/cross.htm) which indicate that he died on a cross, so I contacted the WT and they told me to look at Vine's Expository Dictionary of New Testament Words, and this is what I found.
Topic: Cross, Crucify
<A-1,Noun,4716,stauros>
denotes, primarily, "an upright pale or stake." On such malefactors were nailed for execution. Both the noun and the verb stauroo, "to fasten to a stake or pale," are originally to be distinguished from the ecclesiastical form of a two beamed "cross." The shape of the latter had its origin in ancient , and was used as the symbol of the god Tammuz (being in the shape of the mystic Tau, the initial of his name) in that country and in adjacent lands, including . By the middle of the 3rd cent. A.D. the churches had either departed from, or had travestied, certain doctrines of the Christian faith. In order to increase the prestige of the apostate ecclesiastical system pagans were received into the churches apart from regeneration by faith, and were permitted largely to retain their pagan signs and symbols. Hence the Tau or T, in its most frequent form, with the cross-piece lowered, was adopted to stand for the "cross" of Christ.
As for the Chi, or X, which Constantine declared he had seen in a vision leading him to champion the Christian faith, that letter was the initial of the word "Christ" and had nothing to do with "the Cross" (for xulon, "a timber beam, a tree," as used for the stauros, see under TREE).
The method of execution was borrowed by the Greeks and Romans from the Phoenicians. The stauros denotes (a) "the cross, or stake itself," e.g., Matt. 27:32; (b) "the crucifixion suffered," e.g., 1 Cor. ,18, where "the word of the cross," RV, stands for the Gospel; Gal. , where crucifixion is metaphorically used of the renunciation of the world, that characterizes the true Christian life; Gal. ,14; Eph. ; Phil. .
The judicial custom by which the condemned person carried his stake to the place of execution, was applied by the Lord to those sufferings by which His faithful followers were to express their fellowship with Him, e.g., Matt. 10:38.
<B-1,Verb,4717,stauroo>
signifies (a) "the act of crucifixion," e.g., Matt. ; (b) metaphorically, "the putting off of the flesh with its passions and lusts," a condition fulfilled in the case of those who are "of Christ Jesus," Gal. , RV; so of the relationship between the believer and the world, Gal. .
<B-2,Verb,4957,sustauroo>
"to crucify with" (su, "for," sun, "with"), is used (a) of actual "crucifixion" in company with another, Matt. 27:44; Mark ; John (b) metaphorically, of spiritual identification with Christ in His death, Rom. 6:6; Gal. .
<B-3,Verb,388,anastauroo>
(ana, again) is used in Heb. 6:6 of Hebrew apostates, who as merely nominal Christians, in turning back to Judaism, were thereby virtually guilty of "crucifying" Christ again.
<B-4,Verb,4362,prospegnumi>
"to fix or fasten to anything" (pros, "to," pegnumi, "to fix"), is used of the "crucifixion" of Christ, Acts .