@MBloch's answer is Halachicly right. However, I and my Chevrutah have found an interesting theoretical distinction that must be made when approaching the Sugyah, not found in Halachic polemics on the subject:
Let's start with Mbloch's answer - all things attached go with the house - "The gold-plated faucets as would the built-in air conditioning unit". I'd like to connect it to a famous Mchlokes about paying for breaking your neighbor's window. According to the commonly accepted approach, we can only evaluate the damage relative to the difference in house price. Therefore, if one breaks a window or steals a faucet, since the price of the property stays pretty much the same, no damage is made and no damages are paid.
Many Rabbis (see Chazon Ish) felt injustice and ruled that the incurred damages must be paid anyway. And here I'd like to explain the difference between the approaches:
When we think of a house we can address it from two opposite views: the house as a property (קרקע) and a house as a dwelling (שימוש). For example, as long as we dwell in a house, we don't care about its price, we care about its uses. So if a window is broken or a faucet is stolen that seriously damages the perceived value of the "usability" of the house, not its market value, and vice verse, if we sell the house, the opposite is true.
And that would be the difference between selling a house as property or selling a house for use (renting): for selling a house as property, only things that are connected (considered קרקע) go with it, but when selling for use (renting), everything that defines a "usable" house (as MB noted, by what's accepted in the area), go with it, like the fridge, the appliances, the TVs and the internet infrastructure, etc - everything that's present is included (unless stated otherwise).
This is but THEORETICAL OVERVIEW of the Sugyah and the two approaches. One should always consult a Rabbi and a lawyer when buying/selling/renting property.