How do monks transcend the desire for relationships & sex?

Is it with metta towards the opposite sex or just seeing the unattractiveness of it that craving reduces?

I think it's both of those -- with "unattractive" meaning:

• Something like graveyard meditation
• Seeing it as dissatisfactory (dukkha) or "not permanently satisfying"
• Seeing consequences

I get the impression from watching some of Ven. Yuttadhammo's videos that it's also a matter of developing some dispassion towards "feeling".

And I think perhaps it's a matter of discipline (e.g. the vinaya) as an alternative to pursuing sensuality.

Another example of that, for a monk, is feeling hungry and yet not eating (except properly).

I suppose it's also a matter of habit, changing or attenuating existing habits (if any), and avoiding causes or occasions (e.g. being alone with a woman).

How is sexuality & 'relationship craving' effectively dealt within a monk?

It's easier to start dealing with this while still a lay person. Robes are not a guard against sensual delights. The Vinaya provides strong guards observed by avoiding sensual situations, but practicing restraint and relinquishing before going forth are quite helpful.

The drawback of Western society is that we have coined the term "sexual needs" by elevating sexual desire to the level of food. As Sariputta said in DN33:

All sentient beings are sustained by food.

Sexual desire is not mentioned in the above. Just food. Therefore "sexual needs" is a delusional mask for sexual desire. Sexual desire is fire, and like all fire is best restrained while small. It's easier to put out a match than a burning house. Indulging in sexual desire is like quenching a fire by letting it burn the house down. This is why understanding dependent origination can really help deal with sexual desire. The earlier we understand that we are hooked by desire, the earlier and easier the escape.

To understand where desire starts, we have to understand how it grows:

As long as consciousness remains, it remains involved with form, supported by form, founded on form. And with a sprinkle of relishing, it grows, increases, and matures.

Notice the part that form plays in consciousness. Sexual desire manifests as a craving for particular forms (e.g., we may desire people having a certain shape or sound or smell or feeling). In other words, we indulge in a prejudice of favoritism and aversion in our relationships, prizing desirable people over undesirable people.

The drawback of that desire is prejudice. Prejudice is divisive. The escape from that desire is non-prejudice. By dismantling and relinquishing our prejudices, we can escape the torment of sexual desire. We can make friends with those we might otherwise ignore. We can avoid unethical yet attractive people. We can see that attraction diminishes with age and infirmity. We can even go to the rather intense contemplation of impermanence and decay:

It’s when a mendicant preserves a meditation subject that’s a fine foundation of immersion: the perception of a skeleton, a worm-infested corpse, a livid corpse, a split open corpse, or a bloated corpse.

However, since we live in a world that fears and shuns the contemplation of bloated corpses, it may be easier to work on prejudices. Find the beauty in those you would otherwise avoid. After a time, you might see beauty everywhere and experience a desire for nothing in particular.

They're focused only on beauty. This is the third liberation.

Regarding relationships as needs, notice that relationships are defined by giving. And the highest form of giving is:

But they give a gift thinking, ‘This is an adornment and requisite for the mind.’

This includes the gift of alms food. Food sustains sentient beings. Yet monks receiving alms food must also know that food to be an adornment, impermanent and uncertain. Understanding the impermanence and uncertainty of the gift of food provides a daily and powerful encouragement to reduce relationship craving. A monk is necessarily grateful to all who provide alms food--that too erases prejudice and craving. And that gratitude also encourages monks to offer the gift of Dhamma to all in return for the gift of alms food. This is the best relationship.

And yes. That was all in DN33