Blocking on facebook is a pretty nuclear thing - if a person is logged into their facebook account they cannot even FIND your account. No picture, no name, no nothing. If they are not logged into their facebook account, then they can see whatever your privacy settings allow - for example if you've set your profile to show your face and name to everyone, that includes those without facebook accounts (or people who are not logged into facebook).
Blocking not only prevents the other person from seeing your wall, your pictures, your comments on your friends wall, etc, it also prevents YOU from seeing their stuff. It works both ways.
I'm not sure how it works with 3rd party applications, for example my newspaper allows people to post comments on articles that the paper has published online, using their facebook profile thumbnail and name. My guess is I could still see him there.
Below I'm posting some quotes off facebook's privacy help pages:
Facebook will allow you to block someone who isn't your friend if you know their email:
"What if I can't find the person I want to block?
If you're having trouble finding the person you want to block, you can also block someone by submitting their email address. Go to the Privacy Settings page and click Manage Blocking to the right of Blocked People and Apps. Enter the email address of the person you want to block in the Email field and click Block.
If the email address you submit is associated with an account, that person will be blocked. If the email address isn’t associated with an account, then the person will be blocked if they open an account in the future. Unfortunately, for privacy reasons, we’re unable to provide information about any accounts that may be associated with a blocked email address.
Besides blocking, there are other ways to control who can see the things you post on your timeline. Learn more about your Privacy Settings."
Facebook states "Once you block someone, that person can no longer see things you post on your timeline, tag you, invite you to events or groups, start a conversation with you, or add you as a friend. Note: Does not include apps, games or groups you both participate in."
"Blocking is reciprocal, so you also won't be able to do things like start a conversation with them or add them as a friend. Keep in mind that blocking someone may not prevent all communications or interactions such as in apps or groups and only affects your experience on Facebook, not elsewhere on the web. "
"Blocking someone prevents many types of interactions between you and that person. However, for technical reasons, there are certain instances when someone you’ve blocked may be able to view your comments on the site and vice versa, including comments on a mutual friend's photo or post. "
"After I block someone, can I see anything about that person?
Yes. Blocking allows you to prevent many interactions with someone on Facebook, but you may still encounter content they’ve shared.
Here’s what you might see:
Messages: Your message history with someone you’ve blocked will stay in your inbox. If the blocked person is ever included in a conversation with a group of friends, you’ll be able to see the message. Remember, you can leave a conversation that you don’t want to be part of, or delete a conversation that you don’t like.
Mutual friend stories: There’s a chance that you'll see stories about the blocked person through mutual friends. For example, if the blocked person tags a mutual friend in a photo, you might see this story on your friend’s timeline.
Photos: You might see photos or tags of the blocked person added by other people.
Groups: Someone you’ve blocked won’t be able to add you to a group, but you’ll be able to see groups that the blocked person created or is a member of.
Events: Someone you’ve blocked won’t be able to invite you to an event, but you’ll be able to see events to which both you and the blocked person are invited.
Games and apps: Since games and apps are run by outside developers, the Facebook block won't apply to them. So you could see someone you blocked while you're playing a game (for example, in the game's chat room). "
WH asked me if I had deactivated my facebook account. So he revealed he had looked for me on facebook recently and couldn't find me. My response was "I don't want to talk about facebook"