  Let $\mathfrak g$ be a Borcherds-Kac-Moody Lie superalgebra (BKM superalgebra
in short) with the associated graph $G$. Any such $\mathfrak g$ is constructed
from a free Lie superalgebra by introducing three different sets of relations
on the generators:
  (1) Chevalley relations,
  (2) Serre relations, and
  (3) Commutation relations coming from the graph $G$. By Chevalley relations
we get a triangular decomposition $\mathfrak g = \mathfrak{ n_+} \oplus
\mathfrak h \oplus \mathfrak n_{-}$ and each roots space $\mathfrak{
g_{\alpha}}$ is either contained in $\mathfrak{n_+}$ or $\mathfrak{ n_{-}}$. In
particular, each $\mathfrak{ g_{\alpha}}$ involves only the relations (2) and
(3). In this paper, we are interested in the root spaces of $\mathfrak g$ which
are independent of the Serre relations. We call these roots free roots$^{1}$ of
$\mathfrak g$. Since these root spaces involve only commutation relations
coming from the graph $G$ we can study them combinatorially. We use heaps of
pieces to study these roots and prove many combinatorial properties. We
construct two different bases for these root spaces of $\mathfrak g$: One by
extending the Lalonde's Lyndon heap basis of free partially commutative Lie
algebras to the case of free partially commutative Lie superalgebras and the
other by extending the basis given in \cite{akv17} for the free root spaces of
Borcherds algebras to the case of BKM superalgebras. This is done by studying
the combinatorial properties of super Lyndon heaps. We also discuss a few other
combinatorial properties of free roots.
