Anton Baumstark was a liturgical scholar of the old school, who did not believe that tinkering with the sacred cult was the proper concern of liturgists, but that on the contrary one ought be not master but student of the liturgy. (One may note in passing that Our Lord Jesus Christ is the One Liturgist - Λειτουργὸς - as Hebrews viii, 2 attests.)
Famously, he formulated two laws describing the organic evolution of the liturgy over time: first, that on the most solemn days the most ancient and sober rituals tend to be retained; second, that over time, newer liturgical developments can tend to replace by degrees older features of the divine cult. For instance, until the post-Conciliar reforms, the Divine Office of the last three days of Holy Week, and of the whole of Easter Week, was marked by a simplicity of form unchanged for many ages - no hymns were sung, no short chapters read at the Day Hours, and so forth - this being an example of his first law. Contrariwise, the ancient Roman ferial Office has over time gradually been replaced by a multiplicity of saint's days, so that the weekly cycle of ferial Vesper hymns focussing on the Six Days of Creation are hardly ever sung through in one week, being replaced by hymns for the various occurring saints from their respective Common or Proper.
Baumstark's second law was well-explained by Jungmann, when considering the place of the Lord's Prayer, preces and Collect in the Divine Office. (I write here not of Matins, which was not generally read apart from Lauds - its union with the latter being the ideal, as even its name suggests.) According to mediæval testimony, at the Lateran Basilica the Lord's Prayer was said at the end of each Hour of the Office, with no collect at all appended. It is conjectured that this was the case especially if no priest were present (note here that monks, such as those who sang the Office at the Lateran, were originally unordained), and that in the remote past the Lord's Prayer was the normal conclusion of each Hour - a Collect proper to the day or time being added, at first to give greater solemnity, and then more and more often, so the Lord's Prayer became in the nature of a preface to it. (As the priest first said Dominus vobiscum before the Collect, the Collect itself savoured of things sacerdotal, and was only by degrees, it is argued, accepted as right for a layperson to say: and then it is prefixed with Domine exaudi instead.) The Benedictine and Dominican Breviaries still retain this characteristic pattern of Pater before Collect at the Day Hours.
However, in these, and in the Roman Breviary when the Lord's Prayer still rarely makes an appearance, the Pater noster is always preceded by a threefold Kyrie eleison, Christe eleison, Kyrie eleison. It is thought that this - like the Kyrie at Mass - was once a full litany (as in the Byzantine Rite), but over time was abbreviated to this simple form (St Benedict in his Rule terms it a litany). This litany before the Pater noster disappeared, only to be replaced, apparently under Celtic influence, with suffrages or preces recited after it - originally, these were a series of petitions, each followed by a versicle and response (usually from the psalms), but over time were reduced to a dialogic pattern of versicles and responses.
The Carthusian Breviary retained these long preces at all Hours; but outside that austere Order, it was felt increasingly that preces were not so appropriate to feast days, and so were restricted to ferias in various Breviaries, then were cut down in length (especially at the Little Hours), then were restricted to penitential days, and acquired a penitential sense - since one knelt to pray them, days when they were said were termed "kneeling days". By the mid-twentieth century, the Roman Breviary was being shortened by "simplification of the rubrics" - and the preces at the Little Hours, including the longer and more specialized ones at Prime and Compline, were finally abolished, while Lauds and Vespers only kept their preces on most Ember Days, plus ferial Wednesdays and Fridays of Advent and Lent. In the Roman Breviary, moreover, the Lord's Prayer, from being the original concluding prayer of prayers, had become considered as but part of these preces - and so was in essence discarded altogether from its ancient place.
In the Little Office of Our Lady (itself a pious addition to the daily Office, that became as it were a separate spin-off more suited to lay use because of its relative brevity, simplicity and devotional quality), until the last pre-Conciliar reforms what survived before the Collect of each Hour was not the Lord's Prayer at all, but rather the threefold Kyrie that itself had been a later preface to the Pater noster.
In a separate development, for long centuries (until the last changes under John XXIII before the Council) a Pater and later an Ave had been said as a preparation before each Hour (also a Credo at some Hours), and a Pater with versicle after it... and this, from being a pious custom lifting up the mind to God (as St Ignatius analogously directs before meditation) beforehand, and prolonging the official liturgical prayer, became a fixed devotion, part of the Office. The Lord's Prayer having disappeared from its first place in the Hours, it reappeared elsewhere, finally almost being removed entirely. (In the modern Divine Office, which in many ways represents a decided break with the traditional, organic development of the liturgy, the Lord's Prayer is said aloud, after some intercessions, and before the Collect, but at Lauds and Vespers only, for somewhat artificial reasons.)
As Jungmann summarizes Baumstark's second law, A becomes Ab, Ab becomes AB, this becomes (A)B and finally B alone remains - A being the original liturgical prayer, first b then B being the addition to it that gradually expands in importance until it takes its place entirely.
Another example of this law is the way that, while the more conservative Roman Rite Divine Office still largely consists of the recitation of the psalms, in the Byzantine Rite, the various Canons and divers troparia, kontakia and whatnot - liturgical hymns, of great dogmatic value - have so multiplied that it is they, not the psalms, that are the chief feature of the Hours: indeed, usually the kathisma(ta) or portion(s) of the psalms appointed are very hurriedly recited in monotone by a reader even in monasteries, so that the massed choirs can then break forth in magnificent chanting of the ecclesiastical compositions that now have pride of place; and in parish celebrations, very often the psalms to be recited are drastically pruned and abbreviated, being overshadowed by the more recent and popular elements of the services.