Mine is Batman and wonder woman… Just assume my favorite anything probably has Batman 
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I don’t know if it can be considered a 'ship, as they have been established as an item, but for me it’s Batman and Catwoman. Even on Batman '66 there was an attraction between the two of them!
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Harley and Ivy for me. I shipped them since I was pretty young (probably since Batman: TAS), so I was really happy when they became an actual item!
There’s some other LGBTQ+ non-canon ships I have floating around in my head, so I’ll have to see where their current + future writers take them. 
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Look at my icon and take a guess. 
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Considering it’s the ship that got me into shipping in general, for me it’s easily Kara and Lena from the Arrowverse, a.k.a. Supercorp. I’ve already ranted about my love for them a lot in various topics here, but I could keep going forever about just how much I love them together. Their off-the-charts chemistry, the looks they give each each other, the dozens of parallels w/ other canon couples, especially Barry/Iris and Clark/Lois, and just how groundbreaking it’d be to have a Super and a Luthor be together are all reasons why I’ll remain convinced they should’ve been together a long time ago #SupercorpEndgame
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Dick/Babs! 
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Given that Hal Jordan is one of my favorite characters, I’d probably have to say him and Carol Ferris, even though they aren’t always a great couple.
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The one that carried little baby Kal-El from Krypton to Earth.
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slow clap
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Hal and Carol are also one of my favorite couples, even if they aren’t always very good at the couple thing!
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Diana and Steve Trevor. When they’re written well, they have a relationship of equals and support one another always. They have that “unbreakable connection” thing going on. 
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I am more of a SuperWonder. But as a passive 'shipper, I can recognize and run with quality WonderTrev.
I prefer Batman with Talia.
Supes and Lois is very popular, but not really my proverbial cup of tea.
As to SuperCorp, my take is that they are close friends. In life, in battle. I like that they are straight. I am mostly assuming the name implies something more romantic. Because, yes, I can see that sort of thing in the gif posted above. It’s just not the rabbit hole i would take when pondering said SuperCorp.
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Robin & Spoiler
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Stephanie Brown and optimism.
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Hal and Carol.
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Zatanna & Constantine
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I prefer Zatanna with Nightwing. Seven Soldiers says it all. She dreams of him.
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Seven Soldiers is amazing but they don’t blatantly refer to the actual act of sex like they do with Z & John. They repeatedly mention Zee & Constantine sacking up countless times in animated movies, shows, comics etc. Nightwing belongs to Starfire or Babs way b4 Zana. I prefer Starfire but that’s a whole other can of worms. What DO u like? Ive really only ever heard what u don’t like. Besides my ship being switched to Nightwing & Zatanna that is? I dream of girls a lot too but nobody says u should definitely marry her. Just tell her u dream about her all of the time lol. That doesn’t work very well with most women.
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