  We prove the pro-$p$ version of the Karras, Pietrowski, Solitar, Cohen and
Scott result stating that a virtually free group acts on a tree with finite
vertex stabilizers. If a virtually free pro-$p$ group $G$ has finite
centralizes of all non-trivial torsion elements more stronger statement is
proved: $G$ embeds into a free pro-$p$ product of a free pro-$p$ group and
finite $p$-group. The integral $p$-adic representation theory is used in the
proof; it replaces the Stallings theory of ends in the pro-$p$ case.
