  A \emph{locally irregular graph} is a graph whose adjacent vertices have
distinct degrees. We say that a graph $G$ can be decomposed into $k$ locally
irregular subgraphs if its edge set may be partitioned into $k$ subsets each of
which induces a locally irregular subgraph in $G$. It has been conjectured that
apart from the family of exceptions which admit no such decompositions, i.e.,
odd paths, odd cycles and a special class of graphs of maximum degree $3$,
every connected graph can be decomposed into $3$ locally irregular subgraphs.
Using a combination of a probabilistic approach and some known theorems on
degree constrained subgraphs of a given graph, we prove this to hold for graphs
of sufficiently large minimum degree, $\delta(G)\geq 10^{10}$. This problem is
strongly related to edge colourings distinguishing neighbours by the pallets of
their incident colours and to 1-2-3 Conjecture. In particular, the contribution
of this paper constitutes a strengthening of a result of Addario-Berry, Aldred,
Dalal and Reed [J. Combin. Theory Ser. B 94 (2005) 237-244].
