If you book for an infant on airlines for long haul flights you expect a cot.
I see that most airlines offer cots to the youngest first.
What happens if there are not any left??
Are you provided with a seat or does the child have to sit on your lap the entire journey?

No, the cots aren't guaranteed at all and you should contact your airline as soon as you book to try to reserve the bulkhead seats that have access to the bassinets. If you don't get one then they will be sitting in your lap. With airplanes flying at capacity almost all of the time now, there are few free seats available, but you could try taking a car seat up to the gate. Ask if there's a free seat for you to use your car seat. And if there's not, then you can send the car seat underneath into baggage and get it when you arrive at your destination.
David Robert Hogg,
Publisher of My Little Nomads - the travel with kids website

I've flown with young infants more times than I can count and I have NEVER received this mythical object called a cot. I've heard every airline excuse in the book, but never got a cot. Unless you buy a seat, your chances of getting a seat for your baby totally depend on how full the flight is and how nice the gate agents are. More and more, I'm finding that gate agents are not amenable to scrounging up a seat for unticketed infants. Plus, unless you have a car seat for them, an adult seat isn't going to do you any good, since they're too little to buckle in.
One strategy is to just bring your car seat along anyway, in hopes of getting a spare seat. If they don't have one, you can gate check the car seat -a courtesy airlines generally do for free.
So yes, barring good luck and good will, you will have to keep your baby on your lap for the whole journey. Far from ideal, but you can make it a bit better with some sort of front carrier or sling.
Good luck and bon voyage!

I used to get them a lot when my eldest daughter was little but that was back in 1999/2000 and mostly on domestic (Australian) flights. Once she got to toddler stage I only rarely had to sit next to someone. They would usually block the seat beside someone with a baby or toddler - not just for the sake of the parent but for the person next to the parent who probably doesn't want to be slobbered over etc. Maybe enquire with the airline as to which flights are least likely to be fully subscribed to maximise your chances. Otherwise if it is a really cheap fare, consider coughing up for an extra seat. Depending on the length of your flight, you might find it is well worth the extra money.
we have used air plane cots but always stated clearly when booking that we needed one. That reservation was always honoured. Cots only hold babies up to 9kg or so.
If you don;t book a seat and you don't reserve a cot for your child, they'll sit in your lap! simple.

I have also taken infants on flights alot. There was only one flight where we weren't given a bassinet because there weren't any available. Although in theory this is based on age, we were sitting close to a couple with a child much older than mine who had been given one - and the child didn't even fit into the bassinet. Although there are no guarantees about bassinets / extra seats, I have only been on two flights where I couldn't get an extra seat beside me. Now I prebook seats in the middle somewhere as they tend to be the last to fill-up. If it is a big concern then I would check when the less-busy flights may be.

I've booked a bassinet and on check in been told there were none available. Fortunately I had an empty seat next to me so my daughter slept with her head on my leg across the empty seat (with the arm rest up).

I would call the airline several times before you travel to ensure that you have been allocated a cot. You could also ask them what their policy is on this and whether or not you are guaranteed a cot. I travelled with my then 8-month-old from Australia to the UK and I can tell you, I wouldn't have survived without that cot! She slept for about 80% of the time. Godsend. Good luck! Be assertive.

We had a bassinet for our daughter when we flew with KLM to the USA in 2009. We were told it would be distributed to the youngest person on board, so we were lucky. However, on the return trip the head stewardess told us she couldn't use the bassinet because she was too big. Because it was an overnight flight, our daughter ended up sleeping on my wife's lap all the way home.