Q1
Have AIX 4.3.3 installed and 2 each 9GB hard drives to play with.

Trying to install AIX upgrade 4330011.tgz

Used SMIT logical volume manager to increase hd3 to 501 logical
partitions which should be about 8GB total size.  hd3 is mounted on
/tmp.

CDROM containing 4330011.tgz mounted successfully.  Try to copy the
.tgz file to /tmp with the following command:

cp 4330011.tgz /tmp  and I get the error message:  There is not enough
space in the file system.

A1
501 logical partitions would give you about 8GB if the partition size
is 16MB.  If the partition size is only 4MB (a fairly typical value for
AIX), then you'll have a 2GB logical volume.  Where did the 4330011.tgz
file come from, and what size is it?  The 4330011.tar.gz file from IBM
is 271,108,993 bytes, so even a 2GB logical volume should be plenty big
enough.

My preference is to do the "gunzip" step before writing the CD-ROM,
then extracting the contents of the tarball to your AIX space -- you'll
need about 400MB of free space for the contents of the 4330011.tar
archive.  I wouldn't mount hd3 over /tmp, either, I'd make another
mount point (/mnt/maint, for example) and mount hd3 there.  IBM
recommends that you mount your filesystem at /usr/sys/inst.images, see
https://techsupport.services.ibm.com/server/mlfixes/43/11/00to11.html
for details.

A2
it is very easy to expand a filesystem and the underlying logical volume 
with a single command.
("chfs -a size=<number of 512byte blocks> /<mountpoint>").
The actual size will be rounded to full logical partitions. With the 
standard parameters a LP will be 16 MB on 9G disks.

The whole disk will be divided in less or equal 1014 LPs and all disks 
in a volume group *must* share their LP size. So you cannot add a 18GB 
drive to a rootvg created on a 4GB disk (without altering TFACTOR) for e.g.

But!!!
It may be hard to impossible to shrink a filesystem to free up diskspace 
for expanding another filesystem. For normal usage a 1 or 2 GB /tmp fs 
is wasted.

So it is best practice to create another temporary filesystem through 
smit(ty) and simply delete it afterwards.

If you mount your temporary filesystem to /usr/sys/inst.images smit(ty) 
will automatically find it. Else you must point smit(ty) to the used 
directory.

This is in other words what Rick wrote.
All this applies to all versions of AIX and is machine independand.
TFACTOR can be changed only for AIX 4.3 or newer.