partitioning drive to install Mavericks, but no Mac OS X installation disc

hold the option key on boot, you should then see the Recovey HD

Then you don't have a recovery partiton.

Do you have access to another Mac?

If not, are you near an AppleStore?

ok, but first plug in the TM drive and hold option on boot, you may have a Recovery Partition on the TM Drive.

If not, I was thinking you could use Target Disk mode, but I don't think that that will work.

You may have to make a trip to an AppleStore, unless somone else has a better idea

AppleStore is the easiest way.

Otherwise, you have to Start your Mac in Target Disk Mode, connect to the Other Mac, then on the other Mac, use Disk Utility to Partition your drive (per above), then d/l OS X Mavericks on the other Mac, and when the installer runs, install Mavericks on your Mac, then Boot your Mac and use Migration Assistant to copy data from your TM Drive

AppleStore is the easiest way.

(but they'll probably charge you a fee)

You should re-partiton to G.U.I.D. even if you stay on Lion.

The installer you linked is the Moutain Lion Combo update, it's not the installer.

Are you running Lion (10.7.5) or Mountain Lion?

Did you Purchase Lion on AppleStore? (If you did, there is a way to save the Installer to a USB thumb drive (or DVD), you can then boot from the USB (or DVD) to partition and re-install Lion, then you can upgrade (free) to Mavericks (this is basically the same as what I suggested with using another Mac and Target Disk mode).

If you want to try this, this is what you do.

1) In the App Store->Purchases Tab, re-download Lion (it may say Install, that's ok)

2) After d/l, it will may start the install proress, if it does do not select Continue, instead Quit the Application

3) Create an Install USB using these instructions: How to make a bootable Lion install disc or drive

4) You can now do what was discussed above:

Oh yeah, if you want to go straight to Mavericks, you can create a bootable Intall USB:

See: How to make your own bootable Mavericks USB install drive

or: How to make a bootable Mavericks install drive

(This is a better solution than re-installing Lion)

Then, as above:

1) Boot into the Maveicks Installer (hold option on boot), then select Utilities->Disk Utility

2) Select 1 Partition, Make sure that [Options] has G.U.I.D. selected

3) Select Apply (This will erase the drive, you have a TM Backup, correct?)

4) Quit Disk Utility, then select Reinstall OS X from a Time Machine Drive

5) Install the Firmware Update

Opps, edit 4) from select Reinstall OS X from a Time Machine Drive toInstall OS X Mavericks. During the Install, you will be given the option to Transfer your data from a Time Machine Drive.