AAGHH!.. Headstock broken off!

DONT PANIC! This is probably the most common repair of any experienced luthier. Particularly GIBSON LES PAUL's. They are heavy and mahogany is about as soft a hardwood as you can get in a guitar. They can break of with very little effort.
Luckily, they glue back on just as quickly (in the right hands) although the repair will always be slightly visible... unless painted over with a "solid" colour of course. But if you are lucky, and the head is still attached, the repair (if done immediately) can be almost invisible... and usually at an affordable price.
Remember, the quicker it's repaired... the cheaper it is to do.
A simple "glue it on and smooth it over repair" on a cheap guitar is... well, cheap. The expense is in the refinishing, so this is usually reserved for expensive or new instruments. It's up to you. Either way, the repair is structurally solid and at least as strong (or stronger) as it was before, so no need to worry about a weak headstock.

These points are important if you have a broken headstock...

• As soon as it breaks, loosen the strings as soon as possible
• Try not to move the headstock (if still attached) avoid damaging the broken surfaces
• Carefully search for and keep safe, any small pieces that have fallen off
• Protect any pointed or ragged edges of the break from further damage, this is vital to the quality of the appearance of the repair
• GET IT REPAIRED IMMEDIATELY if possible. The two parts can expand or contract at different rates due to moisture in the air and make it almost impossible to get a smooth joint.

If making a claim for the damage on your insurance,You should take into consideration the fact that the value of the instrument, although just as strong as it was before, will be adversely affected and this should be taken into account when making a claim or if billing another party for the damage.

Cost:

Cost of a basic headstock repair is around £45 - £50 including a very basic setup and strings. This is what 90% of people require and are happy with.

A more complicated repair or/and one that requires a lot of cosmetic work can be as much as £180.00, but I do try to make such an expensive repair as good value for money as I can by including a Class A setup and strings in the price.