  We study the quantum phase transitions of frustrated antiferromagnetic
Heisenberg spin-1 systems on the 3/4 and 3/5 skewed two leg ladder geometries.
These systems can be viewed as arising by periodically removing rung bonds from
a zigzag ladder. We find that in large systems, the ground state (gs) of the
3/4 ladder switches from a singlet to a magnetic state for $J_1 \ge 1.82$; the
gs spin corresponds to ferromagnetic alignment of effective $S = 2$ objects on
each unit cell. The gs of antiferromagnetic exchange Heisenberg spin-1 system
on a 3/5 skewed ladder is highly frustrated and has spiral spin arrangements.
The amplitude of the spin density wave in the 3/5 ladder is significantly
larger compared to that in the magnetic state of the 3/4 ladder. The gs of the
system switches between singlet state and low spin magnetic states multiple
times on tuning $J_1$ in a finite size system. The switching pattern is
nonmonotonic as a function of $J_1$, and depends on the system size. It appears
to be the consequence of higher $J_1$ favoring higher spin magnetic state and
the finite system favoring a standing spin wave. For some specific parameter
values, the magnetic gs in the 3/5 system is doubly degenerate in two different
mirror symmetry subspaces. This degeneracy leads to spontaneous spin parity and
mirror symmetry breaking giving rise to spin current in the gs of the system.
