Eric is the son of Lisa Palmer and friend/neighbor of the Hammonds. He is a nerdy and socially awkward teenage boy who appears to know a lot about disturbing and strange topics, so the Hammonds come to him for information. He tells them that Sheila is undead, and warns them about keeping her fed and the fact that she could become dangerous. He has a crush on Abby Hammond and quickly becomes good friends with her after Sheila's transformation, partnering with her in her instances of rebellion. He also covers the Hammonds in their criminal activities and helps Dr. Cora Wolf cure Sheila.
Eric has always harbored a crush on Abby since they were kids, a point his mother points out frequently. In episode 5 of season 1, Eric kisses Abby, though Abby doesn't reciprocate his feelings admittedly. He plays it off as a "rhetorical exercise" as he continues to help her with her parents or any issue that comes up.
During Season 2, Eric develops a relationship with Ramona who works at the Rite-Aid. She invites him over to her house, only for him to find out she is also undead. To his amazement, Ramona is attracted to Eric and has sex with him. Though Eric begins to harbor feelings towards her, Ramona was only using him to get the serum Sheila and Joel concocted to arrest her undead symptoms and leave to go to Seattle. In the episode "Halibut!," Eric and Abby share a kiss, though Abby was taken aback by the notion and he apologizes profusely.
In Season 3, Eric and Abby pretend to be dating to throw off suspicion of their demolition of the fracking site. The lie becomes too much for them to handle and "break up" in front of the student body. Later though the two begin to grow closer, especially when Ramona returns and demands Eric come with her to Seattle. In the season 3 finale "The Cult of Sheila," Eric helps Abby kill 2 undead intruders in their house and tells her he's okay with the chaos that is in their life and not to exclude him. Abby comes to terms with her feelings towards Eric and spends the night with him at his place. When he asks what's going on, Abby replies "I don't know. I thought maybe we can try and find out. :)"