Boil potatoes until tender, drain, cut into quarters and place in large bowl. Pour in white and vinegar, gently mixing. Allow potatoes to soak up mixture for 5 minutes, then drain away excess liquid.
For pesto, combine parsley, capers, lemon juice & zest and garlic in mini food processor until finely chopped. Pour oil into machine while running in a small stream until fully combined. Season to taste with salt and pepper.
Add pesto into bowl with potatoes and artichokes, toss gently to combine.
Notes
If you prefer not to use wine, just replace with 1/4 cup more of the white wine vinegar.