ecommerce item deleted by user, 301 rediret to HOME PAGE or 404 not found?

I know this question is someway similar to this one where they recommend using 404, but after readingthis other one where they suggest to use 301 when changing site URLs (in the specific case was due to redesign/re factoring) I get a bit of confused and I hope someone could clarify for this specific example:

1. Let's say I have an eCommerce site,
2. let's also say the final user inserted some interesting items in the site and the eCommerce webapp created the item pages at the URLs: http://...?id=20, http://...?id=30 etc.
3. Now let's say some of these interesting items got many external links toward them from many other sites because some people found those items very interesting and linked to them.
4. After some years the final user deletes those items, so obviously the pages and URLshttp://...?id=20, http://...?id=30, etc. now do not exist anymore, but still many pages on the web are linking toward them.

What should the eCommerce site do now, just show a 404 page for those items?

But, I'm confused, wouldn't this lose all the Google PR passed by the external links to the items pages? So isn't it better to use 301 redirect to HOME PAGE that at least passes the PR to the HOME PAGE?

EDIT:

Well, according to answers the best thing to do so far is to do a 404/410.

In order to make this question more complete, I would like to talk about a special case, just to make sure I understood. properly.

Let's say the user creates those items again (the ones he previously deleted at point 4), maybe he changes a bit their names and description, but they are basically the same items. The webapp has no way to know these new added items were the old items so it obviously create them as new items with new URLs http://...?id=100, http://...?id=101, does it makes sense at this point to redirect 301 the old urls to the new ones?

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ANOTHER EDIT (It would be VERY IMPORTANT TO UNDERSTAND):

Well according to the clever answers received so far it seems for the special case, explained in my last EDIT, I could use 301, since it's something of not deceptive cause basically the new pages is a replacement for the old page in term of contents. This is basically done to keep the PR passed from external link and also for better user experience.

But beside the user experience, that is debatable (*1), in order to preserve PR from external broken links why not just always use 301, In my understanding Google dislikes duplicated contents, but are we sure that 301 redirect to HOME PAGE is seen as duplicated contents for Google?!

Google itself suggests to redirect 301 index.html to document root so if they consider 301 as duplicated contents wouldn't that be considered duplicated contents too?! Why do they suggest it?

Let me provoke you: “why not just add a 301 to HOME PAGE for every not found page?”

(*1) as a user, when I follow a broken URL from some external link to some website's page I would stick more on this website if I get redirected to HOME PAGE rather than seeing a 404 page where I would think the website does not even exist anymore and maybe I don't even try to go to HOME PAGE of the website.

ANSWER:-

Users first!!! Catering to search engines instead of users is a recipe for failure.

Good usability would be to redirect them to a page that explains that the product doesn't exist anymore and invite them to explore other related items. That way you don't lose the visitor due to a bad link or confusion. After all if they are following a link expecting one thing and are shown another it looks bad for you if you don't handle it properly.

I don't know if 4xx pages pass PR as I haven't seen anything conclusive pertaining to that but if you do you can "spread" the PR that page has by linking to your home page and any other important pages you deem necessary. If you do lose that PR it isn't a big deal. The usability you gain far outweighs whatever benefit the PR offered.

Update

A 301 is exactly what you want to do. It's the same product and by redirecting you make sure the new listing gets the benefits earned by the old page and users can still find the product they are looking for.

Update #2

Doing a 301 redirect for content that isn't found is both semantically incorrect (the content hasn't moved, it simply doesn't exist) and can be confusing to users (they were expecting product X and got your home page instead with no explanation why).

301 redirects do not cause duplicate content issues. They resolve them by alerting search engines that page A has moved to page B.

(*1) as I user, when following a broken url from some external link to a website's page I might stick more to this website if I get redirected to HOME PAGE rather than seeing a 404 page where I would think the webiste does not even exist anymore and maybe I don't even try to go to HOME PAGE of the website.

A much better solution that solves your problem is to show them a custom 404 page that explains the page no longer exists, recommends possible alternatives, and if they don't like any of the possible alternatives invites them to the home page. If they leave anyway then you never had a chance of keeping them in the first place. This solution is the most user friendly and offers you your highest chance of conversion.