  Distributed Ledger Technologies provide a mechanism to achieve ordering among
transactions that are scattered on multiple participants with no prerequisite
trust relations. This mechanism is essentially based on the idea of new
transactions referencing older ones in a chain structure. Recently, DAG-type
Distributed Ledgers that are based on directed acyclic graphs (DAGs) were
proposed to increase the system scalability through sacrificing the total order
of transactions. In this paper, we develop a mathematical model to study the
process that governs the addition of new transactions to the DAG-type
Distributed Ledger. We propose a simple model for DAG-type Distributed Ledgers
that are obtained from a recursive Young-age Preferential Attachment scheme,
i.e. new connections are made preferably to transactions that have not been in
the system for very long. We determine the asymptotic degree structure of the
resulting graph and show that a forward component of linear size arises if the
edge density is chosen sufficiently large in relation to the `young-age
preference' that tunes how quickly old transactions become unattractive.
