re: Tying New Concrete to an Existing Foundation - Yes or No?

I personally don't know crap about this, but I am adding the exact same size patio. I had three concrete guys out yesterday for bids and all three said they would tie it to my slab.

How about a 3 inch slab with a 6 inch footing around the edge?

OP, just make sure you have a footing all around the slab. The footings should be no less the 12" wide and 12" deep. If you are planning to build on top and set post on the corners, use rebar in all footings, wire mess everywhere else. Oh, a 4" slab is fine. Also don't forget to spray for termites before pouring the slab. That is a must here in Louisiana.

a 6" footing should be fine. 1 foot wide....throw a rebar or two in the footing

Reason for the 12" footing is that if you ever want to close in the patio, you can.

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OP, just make sure you have a footing all around the slab. The footings should be no less the 12" wide and 12" deep. If you are planning to build on top and set post on the corners, use rebar in all footings, wire mess everywhere else. Oh, a 4" slab is fine. Also don't forget to spray for termites before pouring the slab. That is a must here in Louisiana.

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This!
You need to have a footing AT LEAST this size if you want to tie a column of any kind into the slab.

Only reason I would dowel into the existing slab is if you're pouring steps or a step pad because you wouldn't want that to separate from the existing slab with settlement. If there's no elevation change from your back door to the new patio I wouldn't try to tie them together. What everyone else said, 4" thick w/ steel mesh to help prevent cracking in the new patio. If consider digging the perimeter footer a little deeper, 8-10". Get some concrete bricks and break them up into pieces to put under the mesh to keep it off the ground when you pour, but any concrete contractor should know to do this.

Only thing I haven't seem mentioned is make sure you get a termite company to spray the dirt before you pour if its going to abut your existing house.

Agree with the footings if the columns are to come later. If not then a lot of the advice in here is overkill for a 20x30 pad. 4" is perfect. Rebar is overkill. If you don't want to mess with the wwm and worry about how it's going to sit in the slab you can also pour with fiber reinforced concrete.

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I guess all those elevated structural slabs designed with one layer of rebar at the center of the slab are hanging on by a wing and a prayer.

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Does this slab have beams under it? is so the beams are supporting the slab. I would guarantee that the rebar is not in the center of the beams. The rebar in the slab it just for temperature and shrinkage reinforcement. When rebar is in the center of concrete it is strictly for temperature and shrinkage. What I'm saying is that for a 4" slab all you need is temperature and shrinkage reinforcement, and wire mesh provides that. No need to add #4 rebar because it is just overkill.

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Does this slab have beams under it? is so the beams are supporting the slab.

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The slab still has to span between the beams.

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I would guarantee that the rebar is not in the center of the beams.

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Countless structural slabs have been designed with a single layer of rebar at the center. Where are you getting this from?