The Asterisk in the Byzantine Liturgy
The use of an asterisk is a feature that is common to liturgies of the Byzantine rite. Archdale King notes that "in the Byzantine rite, an asterisk is a normal liturgical ornament, which is employed to prevent the veil from touching the Eucharistic bread. The Eastern type is formed by two half circles, with a little star suspended in the centre." (The Liturgy of the Roman Church, appendix 1).
It is worth noting that another source suggests that the star suspended in the centre is not universal in the Byzantine rite.
The Byzantine use of the asterisk can be seen here in this image of a Russian liturgy, sitting upon the diskos (or paten):
These are carried in a formal way as part of the "Great Entrance" of the Byzantine liturgy.
The Byzantine form is fairly straightforward, being two pieces of metal attached and bent downward.
The Asterisk in the Roman Rite
In the Roman rite, the asterisk only makes an appearance in the context of the papal liturgy (and so far as I can yet tell, only in the solemn form of papal liturgy, given the context in which it is used, but I am still trying to confirm this), and it has a different form from that described above, having twelve "rays" with the name of an apostle inscribed upon each ray.
It's use is described by Archdale King:
The Pope retires to the throne to make his Communion. The following ceremonies are observed: The cardinal deacon first takes the paten, on which the master of ceremonies has placed the asterisk, elevates it to the height of his forehead so that it may be seen by the people, turns to the right to show it to the Pope, raises it higher in making a semicircle, and then returns to the left in such a way that it may be exhibited for the third time to both the faithful and the Pope.
The subdeacon, kneeling at the gospel side of the altar, receives the paten and asterisk, and takes them to the Pope, his hands covered by a rich veil embroidered with gold (linteum pectoralis). The asterisk is a safeguard in the form of a star, which is placed over the paten as a covering for the Host when it is carried to the throne. It has twelve rays on which are inscribed the names of the twelve Apostles... The Eastern type is formed by two half circles, with a little star suspended in the centre.
The chalice is elevated by the cardinal deacon with the same ceremony as for the paten. Then the master of ceremonies covers the chalice with a gold-embroidered pall, and the deacon takes it to the throne. Two archbishops hold the book for the communion prayers; while a third assists with a hand-candle. The second master of ceremonies removes the asterisk, and the Pope, taking two particles of the Host in his left hand, says: Panem coelestem and Domine non sum dignus.
A closer look at a papal asterisk:
(Image courtesy of Shouts in the Piazza)
Symoblism
The asterisk symbolizes the Star of Bethlehem that pointed to Christ.
In the Byzantine liturgy, the priest censes the asterisk by holding it over the censer, places it back on the diskos and prays the words, "and a star came and stood over the place where the young child was..."
