One of the original ways of gaining “Arms” was by prescription there was no need for a grant.
The Book of St. Albans written before the foundation of the College of Arms states there are four ways to gain “Arms”
1. Arms borne by descent.
2. Arms borne by conquest.
3. Arms granted by a prince or lord.
4. Arms assumed by the bearer.
With regard to the “Arms assumed by the bearer” there are a number of these held by College of Arms and none have been disputed by the Heralds.
The Book of Saint Albans or Boke of Seynt Albans, a compilation dated 1486, also known as "The Book of Hawking, Hunting and Blasing of Arms"
The section dealing with the laws of heraldry, "Liber Armorum" the source of which is alleged to be the works of Nicholas Upton (an English cleric, not a Herald, died abt 1457) entitled "De Studio Militari" , and some unpublished manuscripts known as "Richards Strangeways Book" around 1450.
The College of Arms, London was incorporated in 1484. They are a living, breathing institution who hold regular meetings and are constantly discussing and revising the Laws of Heraldry.
By using the present tense of "there ARE four ways to gain arms" I hope you are not suggesting that anyone can assume a Coat of Arms in the countries which come under the jurisdiction of the College of Arms now?
Assumed arms have no legal validity in modern day, assuming the arms of an extant line lays you open to the possibility of being sued by the family who do have the legal right to use them, or by the Lord Lyon in Scotland.
I will repeat a previous comment.
To have the legal right to use a Coat of Arms (under the jurisdiction of the College of Arms, London)
it is necessary to show, to the satisfaction of the Heralds, at the College of Arms, an unbroken male line of descent, with primary source evidence, from a man to whom arms were granted or confirmed, and ancient assumed arms will have been confirmed, or to petition for a new Grant of Arms, from the Earl Marshal as the representative of the sovereign, who is himself, of course, a lord.