With regular stocks you are correct, when they do secondaries, they dilute earnings because they now split their profit among more shareholders.
With REITs though, the SO's are accretive rather than dilutive.
Think of it like this:
Ms Jane's third grade class invites Ms Jones third grade class to their school for a visit. It's cupcake day and Ms Jane's class has cupcakes but Ms Jone's class doesn't know it's cupcake day so they don't bring any. There are 30 kids in each class.
Now Ms Jane's class has to share their cupcakes and each kid only gets half a cupcake. 30 cupcakes divided by 60 kids equals half a cupcake each. - this is dilution.
Next week though, they visit again, but this time, Ms Jone's kids know it's cupcake day, so they ALSO bring cupcakes. 60 kids with 60 cupcakes = 1 each. This is accretive. This is how REITS work.
This topic has been covered many times, on many REIT boards. The example I used above was actually posted by someone else, but I remembered it because it made sense to me.
One thing to keep in mind once you understand this- Other people STILL think that SO's dilute REIT earnings, so they sell the stock and it drops the price considerably, which is a GIFT to seasoned REIT investors.
I made BIG money last week when ARR did an SO and the price dropped .40 a share, which allowed me to gobble up a truckload at a discount, which I sold just before Ex-Divvy day yesterday. Watch REITs for awhile and you'll see this happens continuously and can reap the rewards.