As an AI language model, I can provide you with a list of 13 baby and kids ecommerce sites that are growing faster than their customers:

1. Maisonette
2. The Tot
3. Lenny Lemons
4. Babylist
5. Fawn Shoppe
6. Faire Child
7. Spearmint Love
8. Scandiborn
9. Rylee + Cru
10. Babyshop.com
11. Melijoe
12. Little Nomad
13. Smallable

These sites offer a variety of products for babies and kids, including clothing, toys, furniture, and accessories. They have all seen significant growth in recent years, indicating a strong demand for high-quality and unique products for children.