How to turn off y-axis in gnuplot?

my goal is to turn off the y-axis of my plot. Tics are placed on the border and I want a small gap before the plot starts. "unset yzeroaxis" somehow doesn't do anything.

Another question is how can I center the numbers of my x-axes? Right now they seem to be left aligned

Code and Output is as follows. Don't mind the axes, the functions are just examples and the scaling is prepared for the data that will be read later.

#-----------------------------------------------
# Spacing
#-----------------------------------------------

mpl_top    = 0.4 #inch  outer top margin, title goes here
mpl_bot    = 0.7 #inch  outer bottom margin, x label goes here
mpl_left   = 0.9 #inch  outer left margin, y label goes here
mpl_right  = 0.1 #inch  outer right margin, y2 label goes here
mpl_height = 1.5 #inch  height of individual plots
mpl_width  = 2.0 #inch  width of individual plots
mpl_dx     = 0.1 #inch  inter-plot horizontal spacing
mpl_dy     = 0.1 #inch  inter-plot vertical spacing
mpl_ny     = 3   #number of rows
mpl_nx     = 3   #number of columns

# calculate full dimensions
xsize = mpl_left+mpl_right+(mpl_width*mpl_nx)+(mpl_nx-1)*mpl_dx
ysize = mpl_top+mpl_bot+(mpl_ny*mpl_height)+(mpl_ny-1)*mpl_dy

# placement functions
#   rows are numbered from bottom to top
bot(n) = (mpl_bot+(n-1)*mpl_height+(n-1)*mpl_dy)/ysize
top(n)  = 1-((mpl_top+(mpl_ny-n)*(mpl_height+mpl_dy))/ysize)
#   columns are numbered from left to right
left(n) = (mpl_left+(n-1)*mpl_width+(n-1)*mpl_dx)/xsize
right(n)  = 1-((mpl_right+(mpl_nx-n)*(mpl_width+mpl_dx))/xsize)


#-----------------------------------------------
# Settings
#-----------------------------------------------

set terminal pdf enhanced color dl 2.0 size xsize,ysize font "Helvetica,12"
set encoding iso_8859_1
set tics scale 0.5

set output 'multiplot.pdf'

set offsets 0.5,0.5
set autoscale fix
set size 1,1
set key
set border
unset yzeroaxis

# define x-axis settings for all subplots
set xrange [0:10]
set xlabel ''
set format x ''
set xtics border out nomirror 2
set mxtics 2

# define y-axis settings for all subplots


#define linestyles
set style line 1 lc rgb "red" lw 2
set style line 2 lc rgb "blue" lw 2

# for csv
set datafile separator ','

# start plotting
set multiplot

#-----------------------------------------------
# subplot  1-3 (oben links)
#-----------------------------------------------

#  set horizontal margins for first column
set lmargin at screen left(1)
set rmargin at screen right(1)
#  set horizontal margins for third row (top)
set tmargin at screen top(3)
set bmargin at screen bot(3)

#set title 'left'

set ylabel 'Konzentration'
set yrange [0:10]
set format y '%g'
set ytics border out nomirror 2
set mytics 2

#set arrow 1 from graph 0, first 0 rto graph 1,0 nohead lt 1 lw 1 lc 0
#set arrow 2 from first 0, graph 0 rto 0, graph 1 nohead lt 1 lw 1 lc 0

plot plot          \
(sin(x)) \
axes x1y1 \
title '' \
with lines lt 1 lc 5 lw 2\
;

#-----------------------------------------------
# subplot  2-3 (oben mitte)
#-----------------------------------------------

#  set horizontal margins for second column
set lmargin at screen left(2)
set rmargin at screen right(2)
#  set horizontal margins for third row (top)
set tmargin at screen top(3)
set bmargin at screen bot(3)

#set title 'right'

set ylabel ''             # no label here
set yrange [0:10]
set format y ''           # no tic labels
set ytics auto
#set mytics 2
unset yzeroaxis

set arrow 1 from graph 0, first 0 rto graph 1,0 nohead lt 1 lw 1 lc 0
set arrow 2 from first 0, graph 0 rto 0, graph 1 nohead lt 1 lw 1 lc 0

plot          \
cos(x) \
axes x1y1 \
title '' \
with lines lt 1 lc 2 lw 2\
;

#-----------------------------------------------
# subplot  3-3 (oben rechts)
#-----------------------------------------------

#  set horizontal margins for first column
set lmargin at screen left(3)
set rmargin at screen right(3)
#  set horizontal margins for second row (middle)
set tmargin at screen top(3)
set bmargin at screen bot(3)

set title ''

set ylabel ''             # no label here
set yrange [0:10]
set format y ''           # no tic labels
set ytics auto
#set mytics 2

set arrow 1 from graph 0, first 0 rto graph 1,0 nohead lt 1 lw 1 lc 0
set arrow 2 from first 0, graph 0 rto 0, graph 1 nohead lt 1 lw 1 lc 0

plot          \
-sin(x) \
axes x1y1 \
title '' \
with lines lt 1 lc 3 lw 2\
;

#-----------------------------------------------
# subplot  1-2 (mitte links)
#-----------------------------------------------

#  set horizontal margins for second column
set lmargin at screen left(1)
set rmargin at screen right(1)
#  set horizontal margins for second row (middle)
set tmargin at screen top(2)
set bmargin at screen bot(2)

set title ''

set ylabel 'Konzentration'
set yrange [0:10]
set format y '%g'
set ytics auto
#set mytics 2

set arrow 1 from graph 0, first 0 rto graph 1,0 nohead lt 1 lw 1 lc 0
set arrow 2 from first 0, graph 0 rto 0, graph 1 nohead lt 1 lw 1 lc 0

plot          \
-cos(x) \
axes x1y1 \
title '' \
with lines lt 1 lc 4 lw 2\
;

#-----------------------------------------------
# subplot  2-2 (mitte mitte)
#-----------------------------------------------

#  set horizontal margins for first column
set lmargin at screen left(2)
set rmargin at screen right(2)
#  set horizontal margins for first row (bottom)
set tmargin at screen top(2)
set bmargin at screen bot(2)

set title ''

set ylabel ''             # no label here
set yrange [0:10]
set format y ''           # no tic labels
set ytics auto
#set mytics 2

set arrow 1 from graph 0, first 0 rto graph 1,0 nohead lt 1 lw 1 lc 0
set arrow 2 from first 0, graph 0 rto 0, graph 1 nohead lt 1 lw 1 lc 0

plot          \
(sin(x))**2 \
axes x1y1 \
title '' \
with lines lt 1 lc 5 lw 2\
;

#-----------------------------------------------
# subplot  3-2 (mitte rechts)
#-----------------------------------------------

#  set horizontal margins for second column
set lmargin at screen left(3)
set rmargin at screen right(3)
#  set horizontal margins for first row (bottom)
set tmargin at screen top(2)
set bmargin at screen bot(2)

set title ''

set ylabel ''             # no label here
set yrange [0:10]
set format y ''           # no tic labels
set ytics auto
#set mytics 2

set arrow 1 from graph 0, first 0 rto graph 1,0 nohead lt 1 lw 1 lc 0
set arrow 2 from first 0, graph 0 rto 0, graph 1 nohead lt 1 lw 1 lc 0

plot          \
(cos(x))**2 \
axes x1y1 \
title '' \
with lines lt 1 lc 6 lw 2\
;

#-----------------------------------------------
# subplot  1-1 (unten links)
#-----------------------------------------------

#  set horizontal margins for first column
set lmargin at screen left(1)
set rmargin at screen right(1)
#  set horizontal margins for first row (bottom)
set tmargin at screen top(1)
set bmargin at screen bot(1)

set title ''

# now set a label and tic marks for the x-axis
set xlabel "x"
set format y '%g'
set xtics add ('0' 0, '2' 2, '4' 4, '6' 6, '8' 8, '10' 10)

set ylabel "Konzentration"
set yrange [0:10]
set format y '%g'
set ytics auto
#set mytics 2

set arrow 1 from graph 0, first 0 rto graph 1,0 nohead lt 1 lw 1 lc 0
set arrow 2 from first 0, graph 0 rto 0, graph 1 nohead lt 1 lw 1 lc 0

plot          \
(sin(x))**2 \
axes x1y1 \
title '' \
with lines lt 1 lc 5 lw 2\
;

#-----------------------------------------------
# subplot  2-1 (unten mitte)
#-----------------------------------------------

#  set horizontal margins for first column
set lmargin at screen left(2)
set rmargin at screen right(2)
#  set horizontal margins for first row (bottom)
set tmargin at screen top(1)
set bmargin at screen bot(1)

set title ''

# now set a label and tic marks for the x-axis
set xlabel "x"
set format y '%g'
set xtics add ('0' 0, '2' 2, '4' 4, '6' 6, '8' 8, '10' 10)

set ylabel ''             # no label here
set yrange [0:10]
set format y ''           # no tic labels
set ytics auto
#set mytics 2

set arrow 1 from graph 0, first 0 rto graph 1,0 nohead lt 1 lw 1 lc 0
set arrow 2 from first 0, graph 0 rto 0, graph 1 nohead lt 1 lw 1 lc 0

plot          \
(sin(x))**2 \
axes x1y1 \
title '' \
with lines lt 1 lc 5 lw 2\
;

#-----------------------------------------------
# subplot  3-1 (unten rechts)
#-----------------------------------------------

#  set horizontal margins for first column
set lmargin at screen left(3)
set rmargin at screen right(3)
#  set horizontal margins for first row (bottom)
set tmargin at screen top(1)
set bmargin at screen bot(1)

set title ''

# now set a label and tic marks for the x-axis
set xlabel 'x'
set format y '%g'
set xtics add ('0' 0, '2' 2, '4' 4, '6' 6, '8' 8, '10' 10)

set ylabel ''             # no label here
set yrange [0:10]
set format y ''           # no tic labels
set ytics auto
#set mytics 2

set arrow 1 from graph 0, first 0 rto graph 1,0 nohead lt 1 lw 1 lc 0
set arrow 2 from first 0, graph 0 rto 0, graph 1 nohead lt 1 lw 1 lc 0

plot          \
(sin(x))**2 \
axes x1y1 \
title '' \
with lines lt 1 lc 5 lw 2\
;
unset multiplot
unset output

Solution

You are explicitly setting multiple times:

set arrow 1 from graph 0, first 0 rto graph 1,0 nohead lt 1 lw 1 lc 0
set arrow 2 from first 0, graph 0 rto 0, graph 1 nohead lt 1 lw 1 lc 0

which is basically nothing else than a yzeroaxis and a xzeroaxis. Simply remove these lines.

Even if you commented these lines out for the first subplot, arrows, labels and objects will be persistent if you start your code from the console again, unless you start your script with a line reset session.

The line xtics center should do it. Otherwise, you have the option offset. Check help xtics.

By the way, once you set a range or another setting, it will be kept for the next (sub)plot. Your are specifying the same thing many times. Your code could be shortened considerably.