The eastern answer to the hospitality problem a closed table creates: the sacrament is restricted and the blessed bread is given to all.
Source The Byzantine Rite: A Short HistoryRobert F. Taft
The strict answer to this question, admission restricted to those in full fellowship with the celebrating church.
First Communion is the moment a Catholic child is admitted to the table this question governs.
Source Catechism of the Catholic Church, 2nd editionHoly Seethe holders' own account
Why this is disputed. The memorialist churches divide among themselves over admission, from a wholly open table to one restricted to the local congregation. Many Baptist congregations in the open tradition welcome any professing Christian regardless of denomination, while closed communion Baptist and Churches of Christ congregations restrict the table to their own baptized members, and the two practices coexist within the same broader memorialist family.
Source Baptist Confessions of FaithWilliam L. Lumpkin
The open answer to this question, admission without requiring membership, confirmation or prior examination.
Anglican admission rules have moved from confirmation, to baptism, to a contested practice of admitting the unbaptised.
Source The Book of Common PrayerChurch of England; ed. Brian Cummings
Reformed churches admitted the baptised in good standing, historically after examination by the elders.
Source The Westminster Confession of FaithWestminster Assemblythe holders' own account
The question of who may come to this table.
Source The Oxford Dictionary of the Christian Church, 3rd revised editionF. L. Cross and E. A. Livingstone (eds.)
The rite whose admission rule this question governs.
Source The Oxford Dictionary of the Christian Church, 3rd revised editionF. L. Cross and E. A. Livingstone (eds.)
The two questions the churches divide on at the table: what is received, and who may receive it. The answers do not line up with each other.
Source Baptism, Eucharist and Ministry, Faith and Order Paper No. 111World Council of Churches, Commission on Faith and Order
Churches confessing transubstantiation have kept the most restrictive admission rule, though the two questions are formally separate.
Source Catechism of the Catholic Church, 2nd editionHoly Seethe holders' own account
The one case in which the church's own discipline of exclusion is set aside, by a ruling of 325.
Source The Canons of the First Council of NicaeaFirst Council of Nicaeathe holders' own account