A connected graph G is said to be arbitrarily partitionable (AP for short) if for every partition (tau_1, ..., tau_k) of |V(G)| there exists a partition (V_1, ..., V_k) of V(G) such that each V_i induces a connected subgraph of G on \tau_i vertices. Some stronger versions of this property were introduced, namely the ones of being online arbitrarily partitionable and recursively arbitrarily partitionable (OL-AP and R-AP for short, respectively), in which the subgraphs induced by a partition of G must not only be connected but also fulfill some additional conditions. A balloon is a 2-connected graph obtained by connecting two distinct vertices by means of several branches, that is by vertex-disjoint paths. In this paper, we investigate the existence of a constant c such that every AP, OL-AP or R-AP balloons with order n has an elementary path whose order is at least n-c for arbitrary n. From our results, we then deduce some properties of the graph resulting from the removal of an articulation pair in a 2-connected OL-AP or R-AP graph.