Larry, I've had pumpkins and winter squash weighing up to about 25 lbs. do just fine on a trellis with no support, but I usually try to support them in some way anyhow.

I've done it all kinds of ways in the past. Here's some things that worked for me:

--I placed a small stepladder in the garden right next to the trellis and slid the winter squash/pumpkin onto the closest rung of the ladder. Then I wrapped burlap or bird netting around the squash and rung of the ladder to the squash couldn't slide off the rung of the ladder. Then I used a bungee cord to attach the ladder to the trellis so the ladder wouldn't fall over. I have done this with a stepladder that was about 3' tall and I've done it with my garden ladder, which is just a really old, rickety 8' tall wooden ladder I bought for $2 at a fire department garage sale. I painted it a bright girly purple so Tim and Chris would know it was not meant to be used as a ladder. (I don't think it would support human weight.) My purple ladder has has a pumpkin on each and every rung some years.

--I filled up Tidy Cat litter buckets with water and snapped the lids shut, in effect creating large, heavy building blocks. Then I stacked up the litter buckets on top of each other until I had reached the right height for the squash to sit upon. It is not the most attractive support, and turns my garden into A Redneck Garden, but it gets the job done.

--If the winter squash or pumpkin is lower to the ground, I've used a lawn chair, or the lawn chair's matching side table (which wasn't very large, but perfect for this use) to support large squash (one was a green-striped cushaw that must have weighed 25 or 30 lbs) and pumpkins.

--If your trellis is sturdy enough to take the weight, you can use some type of fabric---I've used bird netting, burlap, a piece of shade cloth, an old sheet, etc. to make a sling that is tied to the trellis. To ensure my sling stayed attached to the trellis, I used zip ties and pulled them as tightly as I could. All my trellises are supported by 6' or 8' t-posts every 5 to 10' depending on what is growing on them, so I've never had a trellis break, but I've had heavy loads make them bend sometimes.

--If you buy onions or fruit in netting bags, you can save those bags and use them as slings or hammocks to support the winter squash or pumpkin.

Your Brazilian squash is a butternut variety grown commercially in Brazil and can produce very large squash weighing from 15-40 lbs. Baker Creek sold the seeds of them for several years but I don't remember ever seeing a photo of one of them in the catalog. I wouldn't think a 15-20 lb. squash would necessarily need to be supported, but a larger one might.

I've even used a tomato cage to support a large winter squash by putting the tomato cage in the ground as close to the squash fruit as possible, and then tying some sort of cloth--I think I used fabric cut from an old bedsheet--to the top of the cage like a hammock. I then placed the winter squash in the "hammock". I did use two t-posts to ensure the tomato cage wouldn't fall over.

Anything that will support the weight of the winter squash would work as long as it is sturdy enough that it won't blow over in a thunderstorm and heavy enough that it won't float down stream in flooding rain. It can be attached to the trellis or free standing but close to the trellis. In some years when I have grown a lot of winter squash and pumpkins, my garden has had so many supporting items in it to hold the heavy fruit that it sort of looks ridiculous. Luckily, the big squash leaves cover up a bunch of that sort of stuff pretty quickly so that people don't even notice it as much as you'd think they would.
Dawn

Dawn, thanks. It looked like it might rain an hour of two ago, so I took an old Tee shirt and ran a sturdy piece of bamboo in one sleeve and out the other. I then tied a knot in each side of the tail. I pulled it up like a hammock and all looked good, but I just checked again and the Tee shirt has stretched and I am back where I started. I have to do something else because the stem was starting to pull away from the vine. I did find three more squash when I was out there looking around, but I still want to save this one.

I think it was a mistake to try to trellis this plant. I think it is a pretty plant, and also seems hardy. I want to try to grow it again and the seed may be hard to find.

Larry