  For any truncated path algebra $\Lambda$, we give a structural description of
the modules in the categories ${\cal P}^{<\infty}(\Lambda\text{-mod})$ and
${\cal P}^{<\infty}(\Lambda\text{-Mod})$, consisting of the finitely generated
(resp. arbitrary) $\Lambda$-modules of finite projective dimension. We deduce
that these categories are contravariantly finite in $\Lambda\text{-mod}$ and
$\Lambda\text{-Mod}$, respectively, and determine the corresponding minimal
${\cal P}^{<\infty}$-approximation of an arbitrary $\Lambda$-module from a
projective presentation. In particular, we explicitly construct - based on the
Gabriel quiver $Q$ and the Loewy length of $\Lambda$ - the basic strong tilting
module $_\Lambda T$ (in the sense of Auslander and Reiten) which is coupled
with ${\cal P}^{<\infty}(\Lambda\text{-mod})$ in the contravariantly finite
case. A main topic is the study of the homological properties of the
corresponding tilted algebra $\tilde{\Lambda} =
\text{End}_\Lambda(T)^{\text{op}}$, such as its finitistic dimensions and the
structure of its modules of finite projective dimension. In particular, we
characterize, in terms of a straightforward condition on $Q$, the situation
where the tilting module $T_{\tilde{\Lambda}}$ is strong over $\tilde{\Lambda}$
as well. In this $\Lambda$-$\tilde{\Lambda}$-symmetric situation, we obtain
sharp results on the submodule lattices of the objects in ${\cal
P}^{<\infty}(\text{Mod-}\tilde{\Lambda})$, among them a certain heredity
property; it entails that any module in ${\cal
P}^{<\infty}(\text{Mod-}\tilde{\Lambda})$ is an extension of a projective
module by a module all of whose simple composition factors belong to ${\cal
P}^{<\infty}(\text{mod-}\tilde{\Lambda})$.
