As an AI language model, I do not have knowledge about current ongoing trends but here are some timeless border design trends for thank-you cards:
1. Simple and elegant patterns like stripes, dots, or geometric shapes in a single color
2. Floral and botanical designs with intricate details
3. Watercolor washes in pastel hues
4. Hand-drawn borders with calligraphy or cursive writing
5. Metallic foil accents on black or navy cardstock
6. Minimalistic borders with embossed or debossed details
7. Vintage-inspired designs with lace or filigree patterns
8. Vibrant and bold borders in contrasting colors.
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