  Let $f: M \to M$ be a partially hyperbolic diffeomorphism with conformality
on unstable manifolds. Consider a set of points with nondense forward orbit:
$E(f, y) := \{ z\in M: y\notin \overline{\{f^k(z), k \in \mathbb{N}\}}\}$ for
some $y \in M$. Define $E_{x}(f, y) := E(f, y) \cap W^u(x)$ for any $x\in M$.
Following a method of Broderick-Fishman-Kleinbock, we show that $E_x(f,y)$ is a
winning set of Schmidt games played on $W^u(x)$ which implies that $E_x(f,y)$
has full Hausdorff dimension equal to $\dim W^u(x)$. Furthermore we show that
for any nonempty open set $V \subset M$, $E(f, y) \cap V$ has full Hausdorff
dimension equal to $\dim M$, by constructing measures supported on $E(f, y)\cap
V$ with lower pointwise dimension converging to $\dim M$ and with conditional
measures supported on $E_x(f,y)\cap V$. The results can be extended to the set
of points with forward orbit staying away from a countable subset of $M$.
