Detached structures are limited to a single circuit (though it could be a multi-wire branch circuit).

If you need more circuits a panel must be installed.

And . . . the same holds true for a red house.

#10 is most likely the legal wire size for the 30A circuit, but with the length involved, you'd most likely want to size up to #8 to get the voltage drop acceptable.

The sizing for the greenhouse depends on the load expected.

In addition to what Brick, pointed out, if you have more than one circuit in the outbuilding, you'll need to provide a grounding electrode (rods, etc...) for that structure.

Note there are special concerns in Art. 547 to consider here.

i would run 8-3guf with split circut for carport(20/30a cb), and 10-3guf for green house using split circut (20/20a) If you use a subpanel use sqd qo.

What the hell is a SPLIT circuit SMITTY? Perhaps you mean multiwire branch circuit which both brick and eye already mentioned. If the poster is going to use conduit as he stated, he probably does NOT want to use UF. Will you also shut up about Square D. You're making those of us who actually prefer that panel look bad with your incessant spurious drivel.

What is this 'box in the barn'?
Is it a main panel, sub panel or 120v/15amp lighting circuit? The current and voltage service to it must be adequate to be branched off to two more locations, and the power demand of the greenhouse must also be known for a recomendation to be made.

"If you use a subpanel use sqd qo."

Starting to sound like a sales-puke.

Thanks for the comments. I will be feeding from a grounded sub-panel in the barn supplied with 220v from house main. I used to have a clothes dryer in the barn, but pulled it and no longer use the 220 circuit. There will onlly be one light and a 1500 w, 110v heater in the Green House and then a 30 amp draw from a travel trailer plus a yard light on the carport.

Then a 20A MWBC (which will give you two 20A circuits in the greenhouse, one for the light and convenience outlet and the other to plug in the heater) will probably suffice. The subpanel in the barn (presuming it was properly installed there) should be more than sufficient. Neither of these circuits strictly requires a ground system at the out-structure.

#8 for the RV hookup and #10 for the greenhouse should suffice (again, this is sized up because of the long run to keep the voltage drop in line). If you are going to run in conduit, you'll want to run wet rated individual conductors (THWN for example). Your other option is to direct bury some UF. It's all a matter of how deep you want to dig the trench.

sounds good to me, but why dont u just use a baseboard heater?