AIX has a command to change the size of a partition on the fly.

Lets make the root directory 4GB bigger:
bash-3.00# chfs -a size=+4G /
Filesystem size changed to 60555264

Lets look how the filesystem looks:
bash-3.00# df -g
Filesystem GB blocks Free %Used Iused %Iused Mounted on
/dev/hd4 28.88 24.75 15% 5471 1% /
/dev/hd2 4.62 3.23 31% 33600 5% /usr
/dev/hd9var 0.12 0.11 11% 433 2% /var
/dev/hd3 0.12 0.11 11% 66 1% /tmp
/dev/fwdump 0.12 0.12 1% 4 1% /var/adm/ras/platform
/dev/hd1 0.12 0.12 6% 378 2% /home
/proc - - - - - /proc
/dev/hd10opt 32.62 31.39 4% 30128 1% /opt

Lets try to make it another 4GB bigger:
bash-3.00# chfs -a size=+4G /
0516-404 allocp: This system cannot fulfill the allocation request.
There are not enough free partitions or not enough physical volumes
to keep strictness and satisfy allocation requests. The command
should be retried with different allocation characteristics.
Oh, there was not enough free space on the disk partition.

No problem, lets get more free disk space from another partition (from the partition which is mounted as /opt):
bash-3.00# chfs -a size=-4G /opt
Filesystem size changed to 60030976

Now lets try to make the root directory 4GB bigger again:
bash-3.00# chfs -a size=+4G /
Filesystem size changed to 68943872

Lets look how the file system looks now:
bash-3.00# df -g
Filesystem GB blocks Free %Used Iused %Iused Mounted on
/dev/hd4 32.88 28.75 13% 5471 1% /
/dev/hd2 4.62 3.23 31% 33600 5% /usr
/dev/hd9var 0.12 0.11 11% 433 2% /var
/dev/hd3 0.12 0.11 11% 66 1% /tmp
/dev/fwdump 0.12 0.12 1% 4 1% /var/adm/ras/platform
/dev/hd1 0.12 0.12 6% 378 2% /home
/proc - - - - - /proc
/dev/hd10opt 28.62 27.39 5% 30128 1% /opt
bash-3.00#

You can't do that in Windows, Linux or Mac!